Se da la desigualdad:
( x − 3 ) ( x − 1 ) log ( ( cos ( x ) + cos 2 ( π x ) ) + 2 sin 11 5 ( x 2 ) 2 ) ≥ 2 \left(x - 3\right) \left(x - 1\right) \log{\left(\left(\cos{\left(x \right)} + \cos^{2}{\left(\pi x \right)}\right) + \frac{2 \sin^{\sqrt{\frac{11}{5}}}{\left(\frac{x}{2} \right)}}{2} \right)} \geq 2 ( x − 3 ) ( x − 1 ) log ( ( cos ( x ) + cos 2 ( π x ) ) + 2 2 sin 5 11 ( 2 x ) ) ≥ 2 Para resolver esta desigualdad primero hay que resolver la ecuación correspondiente:
( x − 3 ) ( x − 1 ) log ( ( cos ( x ) + cos 2 ( π x ) ) + 2 sin 11 5 ( x 2 ) 2 ) = 2 \left(x - 3\right) \left(x - 1\right) \log{\left(\left(\cos{\left(x \right)} + \cos^{2}{\left(\pi x \right)}\right) + \frac{2 \sin^{\sqrt{\frac{11}{5}}}{\left(\frac{x}{2} \right)}}{2} \right)} = 2 ( x − 3 ) ( x − 1 ) log ( ( cos ( x ) + cos 2 ( π x ) ) + 2 2 sin 5 11 ( 2 x ) ) = 2 Resolvemos:
x 1 = 100.510435418134 − 0.0047674147312816 i x_{1} = 100.510435418134 - 0.0047674147312816 i x 1 = 100.510435418134 − 0.0047674147312816 i x 2 = 68.5297227402575 x_{2} = 68.5297227402575 x 2 = 68.5297227402575 x 3 = − 93.6529547362519 − 0.0504357558232563 i x_{3} = -93.6529547362519 - 0.0504357558232563 i x 3 = − 93.6529547362519 − 0.0504357558232563 i x 4 = 52.2132777167091 x_{4} = 52.2132777167091 x 4 = 52.2132777167091 x 5 = 94.4430446648741 + 0.0239734809090849 i x_{5} = 94.4430446648741 + 0.0239734809090849 i x 5 = 94.4430446648741 + 0.0239734809090849 i x 6 = 40.1269090033684 x_{6} = 40.1269090033684 x 6 = 40.1269090033684 x 7 = − 33.8796199609159 x_{7} = -33.8796199609159 x 7 = − 33.8796199609159 x 8 = 8.08522178928987 + 0.221804327440013 i x_{8} = 8.08522178928987 + 0.221804327440013 i x 8 = 8.08522178928987 + 0.221804327440013 i x 9 = 42.2523150363882 x_{9} = 42.2523150363882 x 9 = 42.2523150363882 x 10 = − 87.4951623536677 + 0.0264918224471817 i x_{10} = -87.4951623536677 + 0.0264918224471817 i x 10 = − 87.4951623536677 + 0.0264918224471817 i x 11 = − 61.6484065733173 x_{11} = -61.6484065733173 x 11 = − 61.6484065733173 x 12 = − 67.8271064885251 − 0.116532580524128 i x_{12} = -67.8271064885251 - 0.116532580524128 i x 12 = − 67.8271064885251 − 0.116532580524128 i x 13 = − 41.919402019937 + 0.253793657662776 i x_{13} = -41.919402019937 + 0.253793657662776 i x 13 = − 41.919402019937 + 0.253793657662776 i x 14 = − 83.8209630426373 x_{14} = -83.8209630426373 x 14 = − 83.8209630426373 x 15 = − 47.8674926836918 x_{15} = -47.8674926836918 x 15 = − 47.8674926836918 x 16 = 90.1676573854581 x_{16} = 90.1676573854581 x 16 = 90.1676573854581 x 17 = − 16.9160112621997 + 0.236091194526466 i x_{17} = -16.9160112621997 + 0.236091194526466 i x 17 = − 16.9160112621997 + 0.236091194526466 i x 18 = − 7.69765946779217 x_{18} = -7.69765946779217 x 18 = − 7.69765946779217 x 19 = 0.0259969878312562 x_{19} = 0.0259969878312562 x 19 = 0.0259969878312562 x 20 = 58.1159652901164 − 0.168943046399089 i x_{20} = 58.1159652901164 - 0.168943046399089 i x 20 = 58.1159652901164 − 0.168943046399089 i x 21 = 28.0383674979943 x_{21} = 28.0383674979943 x 21 = 28.0383674979943 x 22 = 44.3912217448768 − 0.0386843113446253 i x_{22} = 44.3912217448768 - 0.0386843113446253 i x 22 = 44.3912217448768 − 0.0386843113446253 i x 23 = 14.2557271704627 x_{23} = 14.2557271704627 x 23 = 14.2557271704627 x 24 = − 57.6296158327081 x_{24} = -57.6296158327081 x 24 = − 57.6296158327081 x 25 = − 95.3640346092024 x_{25} = -95.3640346092024 x 25 = − 95.3640346092024 x 26 = − 95.6965840882506 x_{26} = -95.6965840882506 x 26 = − 95.6965840882506 x 27 = 73.8767048669985 + 0.159634370423093 i x_{27} = 73.8767048669985 + 0.159634370423093 i x 27 = 73.8767048669985 + 0.159634370423093 i x 28 = 56.5037427905596 + 0.0142885202923343 i x_{28} = 56.5037427905596 + 0.0142885202923343 i x 28 = 56.5037427905596 + 0.0142885202923343 i x 29 = − 5.66932787023074 − 0.0497064137401943 i x_{29} = -5.66932787023074 - 0.0497064137401943 i x 29 = − 5.66932787023074 − 0.0497064137401943 i x 30 = 88.519795836584 x_{30} = 88.519795836584 x 30 = 88.519795836584 x 31 = 26.3451765828346 x_{31} = 26.3451765828346 x 31 = 26.3451765828346 x 32 = − 71.9446304817941 x_{32} = -71.9446304817941 x 32 = − 71.9446304817941 x 33 = 92.1945249026872 x_{33} = 92.1945249026872 x 33 = 92.1945249026872 x 34 = 54.128574941131 x_{34} = 54.128574941131 x 34 = 54.128574941131 x 35 = − 81.5428971975277 − 0.0191245612540122 i x_{35} = -81.5428971975277 - 0.0191245612540122 i x 35 = − 81.5428971975277 − 0.0191245612540122 i x 36 = 15.9671278777495 x_{36} = 15.9671278777495 x 36 = 15.9671278777495 x 37 = 80.3190541652628 x_{37} = 80.3190541652628 x 37 = 80.3190541652628 x 38 = − 73.7353154660035 x_{38} = -73.7353154660035 x 38 = − 73.7353154660035 x 39 = 64.2998397574696 x_{39} = 64.2998397574696 x 39 = 64.2998397574696 x 40 = 35.9079872393627 − 0.212205057974673 i x_{40} = 35.9079872393627 - 0.212205057974673 i x 40 = 35.9079872393627 − 0.212205057974673 i x 41 = − 52.089956603758 − 0.217871757172483 i x_{41} = -52.089956603758 - 0.217871757172483 i x 41 = − 52.089956603758 − 0.217871757172483 i x 42 = 32.2802458587386 − 0.0691505085823875 i x_{42} = 32.2802458587386 - 0.0691505085823875 i x 42 = 32.2802458587386 − 0.0691505085823875 i x 43 = − 66.9212508083606 + 0.269489880500199 i x_{43} = -66.9212508083606 + 0.269489880500199 i x 43 = − 66.9212508083606 + 0.269489880500199 i x 44 = 20.164782218209 − 0.121405581267706 i x_{44} = 20.164782218209 - 0.121405581267706 i x 44 = 20.164782218209 − 0.121405581267706 i x 45 = 92.7122815315705 x_{45} = 92.7122815315705 x 45 = 92.7122815315705 x 46 = − 99.6012951400255 x_{46} = -99.6012951400255 x 46 = − 99.6012951400255 x 47 = 6.38590519069954 − 0.00575895418760668 i x_{47} = 6.38590519069954 - 0.00575895418760668 i x 47 = 6.38590519069954 − 0.00575895418760668 i x 48 = − 54.8953300391768 − 0.186195356732807 i x_{48} = -54.8953300391768 - 0.186195356732807 i x 48 = − 54.8953300391768 − 0.186195356732807 i x 49 = − 31.4961106304242 − 0.0191707060545047 i x_{49} = -31.4961106304242 - 0.0191707060545047 i x 49 = − 31.4961106304242 − 0.0191707060545047 i x 50 = − 14.1170844576311 − 0.166541967937758 i x_{50} = -14.1170844576311 - 0.166541967937758 i x 50 = − 14.1170844576311 − 0.166541967937758 i x 51 = − 23.6954544888424 x_{51} = -23.6954544888424 x 51 = − 23.6954544888424 x 52 = 82.3332156159097 − 0.0540938198971391 i x_{52} = 82.3332156159097 - 0.0540938198971391 i x 52 = 82.3332156159097 − 0.0540938198971391 i x 53 = − 29.8795040594379 − 0.162851569333039 i x_{53} = -29.8795040594379 - 0.162851569333039 i x 53 = − 29.8795040594379 − 0.162851569333039 i x 54 = − 2.07254282841937 − 0.270802694872933 i x_{54} = -2.07254282841937 - 0.270802694872933 i x 54 = − 2.07254282841937 − 0.270802694872933 i x 55 = − 17.7742905308476 − 0.0886248084834091 i x_{55} = -17.7742905308476 - 0.0886248084834091 i x 55 = − 17.7742905308476 − 0.0886248084834091 i x 56 = − 19.4587884353761 x_{56} = -19.4587884353761 x 56 = − 19.4587884353761 x 57 = − 59.9535607517084 x_{57} = -59.9535607517084 x 57 = − 59.9535607517084 x 58 = − 45.7553208896104 x_{58} = -45.7553208896104 x 58 = − 45.7553208896104 x 59 = 111.823557484907 + 0.114305309917005 i x_{59} = 111.823557484907 + 0.114305309917005 i x 59 = 111.823557484907 + 0.114305309917005 i x 60 = 50.4985071395553 − 0.0369607780358167 i x_{60} = 50.4985071395553 - 0.0369607780358167 i x 60 = 50.4985071395553 − 0.0369607780358167 i x 61 = 76.3874647847242 x_{61} = 76.3874647847242 x 61 = 76.3874647847242 x 62 = − 35.7814970140969 x_{62} = -35.7814970140969 x 62 = − 35.7814970140969 x 63 = 11.7207671633765 − 0.0672315020436625 i x_{63} = 11.7207671633765 - 0.0672315020436625 i x 63 = 11.7207671633765 − 0.0672315020436625 i x 64 = − 49.4130262826674 x_{64} = -49.4130262826674 x 64 = − 49.4130262826674 x 65 = − 75.4734559804639 − 0.0125866265148061 i x_{65} = -75.4734559804639 - 0.0125866265148061 i x 65 = − 75.4734559804639 − 0.0125866265148061 i x 66 = 3.28658644133219 − 0.369342697073948 i x_{66} = 3.28658644133219 - 0.369342697073948 i x 66 = 3.28658644133219 − 0.369342697073948 i x 67 = 38.5957978455979 x_{67} = 38.5957978455979 x 67 = 38.5957978455979 x 68 = 5.30170266613166 x_{68} = 5.30170266613166 x 68 = 5.30170266613166 x 69 = − 9.92049181202345 x_{69} = -9.92049181202345 x 69 = − 9.92049181202345 x 70 = 85.9189522586373 − 0.251433509912749 i x_{70} = 85.9189522586373 - 0.251433509912749 i x 70 = 85.9189522586373 − 0.251433509912749 i x 71 = − 25.4194772379531 − 0.0303405831403926 i x_{71} = -25.4194772379531 - 0.0303405831403926 i x 71 = − 25.4194772379531 − 0.0303405831403926 i x 72 = − 55.7122976199228 − 0.0670079176742718 i x_{72} = -55.7122976199228 - 0.0670079176742718 i x 72 = − 55.7122976199228 − 0.0670079176742718 i x 73 = − 37.5022710508658 + 0.0343942270405407 i x_{73} = -37.5022710508658 + 0.0343942270405407 i x 73 = − 37.5022710508658 + 0.0343942270405407 i x 74 = 18.4984592764267 − 0.0265263451148552 i x_{74} = 18.4984592764267 - 0.0265263451148552 i x 74 = 18.4984592764267 − 0.0265263451148552 i x 75 = − 43.6019102829849 − 0.0368709510682677 i x_{75} = -43.6019102829849 - 0.0368709510682677 i x 75 = − 43.6019102829849 − 0.0368709510682677 i x 76 = − 11.6114441043886 x_{76} = -11.6114441043886 x 76 = − 11.6114441043886 x 77 = − 97.9075682228443 x_{77} = -97.9075682228443 x 77 = − 97.9075682228443 x 78 = 70.2194936875721 − 0.0917905796213954 i x_{78} = 70.2194936875721 - 0.0917905796213954 i x 78 = 70.2194936875721 − 0.0917905796213954 i x 79 = − 80.7389286380715 + 0.075669195211865 i x_{79} = -80.7389286380715 + 0.075669195211865 i x 79 = − 80.7389286380715 + 0.075669195211865 i x 80 = − 40.9095455028656 − 0.321103912982183 i x_{80} = -40.9095455028656 - 0.321103912982183 i x 80 = − 40.9095455028656 − 0.321103912982183 i x 81 = − 85.8215792771042 x_{81} = -85.8215792771042 x 81 = − 85.8215792771042 x 82 = 62.5726892695298 − 0.0287324695214719 i x_{82} = 62.5726892695298 - 0.0287324695214719 i x 82 = 62.5726892695298 − 0.0287324695214719 i x 83 = 12.543766196288 − 0.00146153110638568 i x_{83} = 12.543766196288 - 0.00146153110638568 i x 83 = 12.543766196288 − 0.00146153110638568 i x 84 = 78.081604889231 x_{84} = 78.081604889231 x 84 = 78.081604889231 Descartamos las soluciones complejas:
x 1 = 68.5297227402575 x_{1} = 68.5297227402575 x 1 = 68.5297227402575 x 2 = 52.2132777167091 x_{2} = 52.2132777167091 x 2 = 52.2132777167091 x 3 = 40.1269090033684 x_{3} = 40.1269090033684 x 3 = 40.1269090033684 x 4 = − 33.8796199609159 x_{4} = -33.8796199609159 x 4 = − 33.8796199609159 x 5 = 42.2523150363882 x_{5} = 42.2523150363882 x 5 = 42.2523150363882 x 6 = − 61.6484065733173 x_{6} = -61.6484065733173 x 6 = − 61.6484065733173 x 7 = − 83.8209630426373 x_{7} = -83.8209630426373 x 7 = − 83.8209630426373 x 8 = − 47.8674926836918 x_{8} = -47.8674926836918 x 8 = − 47.8674926836918 x 9 = 90.1676573854581 x_{9} = 90.1676573854581 x 9 = 90.1676573854581 x 10 = − 7.69765946779217 x_{10} = -7.69765946779217 x 10 = − 7.69765946779217 x 11 = 0.0259969878312562 x_{11} = 0.0259969878312562 x 11 = 0.0259969878312562 x 12 = 28.0383674979943 x_{12} = 28.0383674979943 x 12 = 28.0383674979943 x 13 = 14.2557271704627 x_{13} = 14.2557271704627 x 13 = 14.2557271704627 x 14 = − 57.6296158327081 x_{14} = -57.6296158327081 x 14 = − 57.6296158327081 x 15 = − 95.3640346092024 x_{15} = -95.3640346092024 x 15 = − 95.3640346092024 x 16 = − 95.6965840882506 x_{16} = -95.6965840882506 x 16 = − 95.6965840882506 x 17 = 88.519795836584 x_{17} = 88.519795836584 x 17 = 88.519795836584 x 18 = 26.3451765828346 x_{18} = 26.3451765828346 x 18 = 26.3451765828346 x 19 = − 71.9446304817941 x_{19} = -71.9446304817941 x 19 = − 71.9446304817941 x 20 = 92.1945249026872 x_{20} = 92.1945249026872 x 20 = 92.1945249026872 x 21 = 54.128574941131 x_{21} = 54.128574941131 x 21 = 54.128574941131 x 22 = 15.9671278777495 x_{22} = 15.9671278777495 x 22 = 15.9671278777495 x 23 = 80.3190541652628 x_{23} = 80.3190541652628 x 23 = 80.3190541652628 x 24 = − 73.7353154660035 x_{24} = -73.7353154660035 x 24 = − 73.7353154660035 x 25 = 64.2998397574696 x_{25} = 64.2998397574696 x 25 = 64.2998397574696 x 26 = 92.7122815315705 x_{26} = 92.7122815315705 x 26 = 92.7122815315705 x 27 = − 99.6012951400255 x_{27} = -99.6012951400255 x 27 = − 99.6012951400255 x 28 = − 23.6954544888424 x_{28} = -23.6954544888424 x 28 = − 23.6954544888424 x 29 = − 19.4587884353761 x_{29} = -19.4587884353761 x 29 = − 19.4587884353761 x 30 = − 59.9535607517084 x_{30} = -59.9535607517084 x 30 = − 59.9535607517084 x 31 = − 45.7553208896104 x_{31} = -45.7553208896104 x 31 = − 45.7553208896104 x 32 = 76.3874647847242 x_{32} = 76.3874647847242 x 32 = 76.3874647847242 x 33 = − 35.7814970140969 x_{33} = -35.7814970140969 x 33 = − 35.7814970140969 x 34 = − 49.4130262826674 x_{34} = -49.4130262826674 x 34 = − 49.4130262826674 x 35 = 38.5957978455979 x_{35} = 38.5957978455979 x 35 = 38.5957978455979 x 36 = 5.30170266613166 x_{36} = 5.30170266613166 x 36 = 5.30170266613166 x 37 = − 9.92049181202345 x_{37} = -9.92049181202345 x 37 = − 9.92049181202345 x 38 = − 11.6114441043886 x_{38} = -11.6114441043886 x 38 = − 11.6114441043886 x 39 = − 97.9075682228443 x_{39} = -97.9075682228443 x 39 = − 97.9075682228443 x 40 = − 85.8215792771042 x_{40} = -85.8215792771042 x 40 = − 85.8215792771042 x 41 = 78.081604889231 x_{41} = 78.081604889231 x 41 = 78.081604889231 Las raíces dadas
x 27 = − 99.6012951400255 x_{27} = -99.6012951400255 x 27 = − 99.6012951400255 x 39 = − 97.9075682228443 x_{39} = -97.9075682228443 x 39 = − 97.9075682228443 x 16 = − 95.6965840882506 x_{16} = -95.6965840882506 x 16 = − 95.6965840882506 x 15 = − 95.3640346092024 x_{15} = -95.3640346092024 x 15 = − 95.3640346092024 x 40 = − 85.8215792771042 x_{40} = -85.8215792771042 x 40 = − 85.8215792771042 x 7 = − 83.8209630426373 x_{7} = -83.8209630426373 x 7 = − 83.8209630426373 x 24 = − 73.7353154660035 x_{24} = -73.7353154660035 x 24 = − 73.7353154660035 x 19 = − 71.9446304817941 x_{19} = -71.9446304817941 x 19 = − 71.9446304817941 x 6 = − 61.6484065733173 x_{6} = -61.6484065733173 x 6 = − 61.6484065733173 x 30 = − 59.9535607517084 x_{30} = -59.9535607517084 x 30 = − 59.9535607517084 x 14 = − 57.6296158327081 x_{14} = -57.6296158327081 x 14 = − 57.6296158327081 x 34 = − 49.4130262826674 x_{34} = -49.4130262826674 x 34 = − 49.4130262826674 x 8 = − 47.8674926836918 x_{8} = -47.8674926836918 x 8 = − 47.8674926836918 x 31 = − 45.7553208896104 x_{31} = -45.7553208896104 x 31 = − 45.7553208896104 x 33 = − 35.7814970140969 x_{33} = -35.7814970140969 x 33 = − 35.7814970140969 x 4 = − 33.8796199609159 x_{4} = -33.8796199609159 x 4 = − 33.8796199609159 x 28 = − 23.6954544888424 x_{28} = -23.6954544888424 x 28 = − 23.6954544888424 x 29 = − 19.4587884353761 x_{29} = -19.4587884353761 x 29 = − 19.4587884353761 x 38 = − 11.6114441043886 x_{38} = -11.6114441043886 x 38 = − 11.6114441043886 x 37 = − 9.92049181202345 x_{37} = -9.92049181202345 x 37 = − 9.92049181202345 x 10 = − 7.69765946779217 x_{10} = -7.69765946779217 x 10 = − 7.69765946779217 x 11 = 0.0259969878312562 x_{11} = 0.0259969878312562 x 11 = 0.0259969878312562 x 36 = 5.30170266613166 x_{36} = 5.30170266613166 x 36 = 5.30170266613166 x 13 = 14.2557271704627 x_{13} = 14.2557271704627 x 13 = 14.2557271704627 x 22 = 15.9671278777495 x_{22} = 15.9671278777495 x 22 = 15.9671278777495 x 18 = 26.3451765828346 x_{18} = 26.3451765828346 x 18 = 26.3451765828346 x 12 = 28.0383674979943 x_{12} = 28.0383674979943 x 12 = 28.0383674979943 x 35 = 38.5957978455979 x_{35} = 38.5957978455979 x 35 = 38.5957978455979 x 3 = 40.1269090033684 x_{3} = 40.1269090033684 x 3 = 40.1269090033684 x 5 = 42.2523150363882 x_{5} = 42.2523150363882 x 5 = 42.2523150363882 x 2 = 52.2132777167091 x_{2} = 52.2132777167091 x 2 = 52.2132777167091 x 21 = 54.128574941131 x_{21} = 54.128574941131 x 21 = 54.128574941131 x 25 = 64.2998397574696 x_{25} = 64.2998397574696 x 25 = 64.2998397574696 x 1 = 68.5297227402575 x_{1} = 68.5297227402575 x 1 = 68.5297227402575 x 32 = 76.3874647847242 x_{32} = 76.3874647847242 x 32 = 76.3874647847242 x 41 = 78.081604889231 x_{41} = 78.081604889231 x 41 = 78.081604889231 x 23 = 80.3190541652628 x_{23} = 80.3190541652628 x 23 = 80.3190541652628 x 17 = 88.519795836584 x_{17} = 88.519795836584 x 17 = 88.519795836584 x 9 = 90.1676573854581 x_{9} = 90.1676573854581 x 9 = 90.1676573854581 x 20 = 92.1945249026872 x_{20} = 92.1945249026872 x 20 = 92.1945249026872 x 26 = 92.7122815315705 x_{26} = 92.7122815315705 x 26 = 92.7122815315705 son puntos de cambio del signo de desigualdad en las soluciones.
Primero definámonos con el signo hasta el punto extremo izquierdo:
x 0 ≤ x 27 x_{0} \leq x_{27} x 0 ≤ x 27 Consideremos, por ejemplo, el punto
x 0 = x 27 − 1 10 x_{0} = x_{27} - \frac{1}{10} x 0 = x 27 − 10 1 =
− 99.6012951400255 + − 1 10 -99.6012951400255 + - \frac{1}{10} − 99.6012951400255 + − 10 1 =
− 99.7012951400255 -99.7012951400255 − 99.7012951400255 lo sustituimos en la expresión
( x − 3 ) ( x − 1 ) log ( ( cos ( x ) + cos 2 ( π x ) ) + 2 sin 11 5 ( x 2 ) 2 ) ≥ 2 \left(x - 3\right) \left(x - 1\right) \log{\left(\left(\cos{\left(x \right)} + \cos^{2}{\left(\pi x \right)}\right) + \frac{2 \sin^{\sqrt{\frac{11}{5}}}{\left(\frac{x}{2} \right)}}{2} \right)} \geq 2 ( x − 3 ) ( x − 1 ) log ( ( cos ( x ) + cos 2 ( π x ) ) + 2 2 sin 5 11 ( 2 x ) ) ≥ 2 ( − 99.7012951400255 − 3 ) ( − 99.7012951400255 − 1 ) log ( 2 sin 11 5 ( − 99.7012951400255 2 ) 2 + ( cos 2 ( ( − 99.7012951400255 ) π ) + cos ( − 99.7012951400255 ) ) ) ≥ 2 \left(-99.7012951400255 - 3\right) \left(-99.7012951400255 - 1\right) \log{\left(\frac{2 \sin^{\sqrt{\frac{11}{5}}}{\left(- \frac{99.7012951400255}{2} \right)}}{2} + \left(\cos^{2}{\left(\left(-99.7012951400255\right) \pi \right)} + \cos{\left(-99.7012951400255 \right)}\right) \right)} \geq 2 ( − 99.7012951400255 − 3 ) ( − 99.7012951400255 − 1 ) log ( 2 2 sin 5 11 ( − 2 99.7012951400255 ) + ( cos 2 ( ( − 99.7012951400255 ) π ) + cos ( − 99.7012951400255 ) ) ) ≥ 2 / ____ \
| \/ 55 |
| ------ | >= 2
| 5 2 |
10342.1534331586*log\0.675119406768933 + 0.403038827677351 + cos (1.70129514002545*pi)/ significa que una de las soluciones de nuestra ecuación será con:
x ≤ − 99.6012951400255 x \leq -99.6012951400255 x ≤ − 99.6012951400255 _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____
\ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \
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x27 x39 x16 x15 x40 x7 x24 x19 x6 x30 x14 x34 x8 x31 x33 x4 x28 x29 x38 x37 x10 x11 x36 x13 x22 x18 x12 x35 x3 x5 x2 x21 x25 x1 x32 x41 x23 x17 x9 x20 x26 Recibiremos otras soluciones de la desigualdad pasando al polo siguiente etc.
etc.
Respuesta:
x ≤ − 99.6012951400255 x \leq -99.6012951400255 x ≤ − 99.6012951400255 x ≥ − 97.9075682228443 ∧ x ≤ − 95.6965840882506 x \geq -97.9075682228443 \wedge x \leq -95.6965840882506 x ≥ − 97.9075682228443 ∧ x ≤ − 95.6965840882506 x ≥ − 95.3640346092024 ∧ x ≤ − 85.8215792771042 x \geq -95.3640346092024 \wedge x \leq -85.8215792771042 x ≥ − 95.3640346092024 ∧ x ≤ − 85.8215792771042 x ≥ − 83.8209630426373 ∧ x ≤ − 73.7353154660035 x \geq -83.8209630426373 \wedge x \leq -73.7353154660035 x ≥ − 83.8209630426373 ∧ x ≤ − 73.7353154660035 x ≥ − 71.9446304817941 ∧ x ≤ − 61.6484065733173 x \geq -71.9446304817941 \wedge x \leq -61.6484065733173 x ≥ − 71.9446304817941 ∧ x ≤ − 61.6484065733173 x ≥ − 59.9535607517084 ∧ x ≤ − 57.6296158327081 x \geq -59.9535607517084 \wedge x \leq -57.6296158327081 x ≥ − 59.9535607517084 ∧ x ≤ − 57.6296158327081 x ≥ − 49.4130262826674 ∧ x ≤ − 47.8674926836918 x \geq -49.4130262826674 \wedge x \leq -47.8674926836918 x ≥ − 49.4130262826674 ∧ x ≤ − 47.8674926836918 x ≥ − 45.7553208896104 ∧ x ≤ − 35.7814970140969 x \geq -45.7553208896104 \wedge x \leq -35.7814970140969 x ≥ − 45.7553208896104 ∧ x ≤ − 35.7814970140969 x ≥ − 33.8796199609159 ∧ x ≤ − 23.6954544888424 x \geq -33.8796199609159 \wedge x \leq -23.6954544888424 x ≥ − 33.8796199609159 ∧ x ≤ − 23.6954544888424 x ≥ − 19.4587884353761 ∧ x ≤ − 11.6114441043886 x \geq -19.4587884353761 \wedge x \leq -11.6114441043886 x ≥ − 19.4587884353761 ∧ x ≤ − 11.6114441043886 x ≥ − 9.92049181202345 ∧ x ≤ − 7.69765946779217 x \geq -9.92049181202345 \wedge x \leq -7.69765946779217 x ≥ − 9.92049181202345 ∧ x ≤ − 7.69765946779217 x ≥ 0.0259969878312562 ∧ x ≤ 5.30170266613166 x \geq 0.0259969878312562 \wedge x \leq 5.30170266613166 x ≥ 0.0259969878312562 ∧ x ≤ 5.30170266613166 x ≥ 14.2557271704627 ∧ x ≤ 15.9671278777495 x \geq 14.2557271704627 \wedge x \leq 15.9671278777495 x ≥ 14.2557271704627 ∧ x ≤ 15.9671278777495 x ≥ 26.3451765828346 ∧ x ≤ 28.0383674979943 x \geq 26.3451765828346 \wedge x \leq 28.0383674979943 x ≥ 26.3451765828346 ∧ x ≤ 28.0383674979943 x ≥ 38.5957978455979 ∧ x ≤ 40.1269090033684 x \geq 38.5957978455979 \wedge x \leq 40.1269090033684 x ≥ 38.5957978455979 ∧ x ≤ 40.1269090033684 x ≥ 42.2523150363882 ∧ x ≤ 52.2132777167091 x \geq 42.2523150363882 \wedge x \leq 52.2132777167091 x ≥ 42.2523150363882 ∧ x ≤ 52.2132777167091 x ≥ 54.128574941131 ∧ x ≤ 64.2998397574696 x \geq 54.128574941131 \wedge x \leq 64.2998397574696 x ≥ 54.128574941131 ∧ x ≤ 64.2998397574696 x ≥ 68.5297227402575 ∧ x ≤ 76.3874647847242 x \geq 68.5297227402575 \wedge x \leq 76.3874647847242 x ≥ 68.5297227402575 ∧ x ≤ 76.3874647847242 x ≥ 78.081604889231 ∧ x ≤ 80.3190541652628 x \geq 78.081604889231 \wedge x \leq 80.3190541652628 x ≥ 78.081604889231 ∧ x ≤ 80.3190541652628 x ≥ 88.519795836584 ∧ x ≤ 90.1676573854581 x \geq 88.519795836584 \wedge x \leq 90.1676573854581 x ≥ 88.519795836584 ∧ x ≤ 90.1676573854581 x ≥ 92.1945249026872 ∧ x ≤ 92.7122815315705 x \geq 92.1945249026872 \wedge x \leq 92.7122815315705 x ≥ 92.1945249026872 ∧ x ≤ 92.7122815315705 
2x^2-6x+4<=0
18(x-2)+33>-7+16x
(x-1)*(x+1)<0