Se da la desigualdad:
((3x+(2x+3))−7)cos(x)>0Para resolver esta desigualdad primero hay que resolver la ecuación correspondiente:
((3x+(2x+3))−7)cos(x)=0Resolvemos:
x1=7.85398163397448x2=−86.3937979737193x3=23.5619449019235x4=−67.5442420521806x5=−4.71238898038469x6=−20.4203522483337x7=0.760491357747641x8=−98.9601685880785x9=−39.2699081698724x10=26.7035375555132x11=−48.6946861306418x12=−89.5353906273091x13=−17.2787595947439x14=20.4203522483337x15=−64.4026493985908x16=14.1371669411541x17=−26.7035375555132x18=−70.6858347057703x19=−32.9867228626928x20=4.71238898038469x21=−95.8185759344887x22=−7.85398163397448x23=−23.5619449019235x24=−36.1283155162826x25=−83.2522053201295x26=−1.5707963267949x27=−58.1194640914112x28=−10.9955742875643x29=1.5707963267949x30=29.845130209103x31=−73.8274273593601x32=−92.6769832808989x33=−54.9778714378214x34=−76.9690200129499x35=−1610.06623496477x36=−61.261056745001x37=17.2787595947439x38=10.9955742875643x39=−51.8362787842316x40=−45.553093477052x41=−42.4115008234622x42=−80.1106126665397x43=−29.845130209103x44=−14.1371669411541x1=7.85398163397448x2=−86.3937979737193x3=23.5619449019235x4=−67.5442420521806x5=−4.71238898038469x6=−20.4203522483337x7=0.760491357747641x8=−98.9601685880785x9=−39.2699081698724x10=26.7035375555132x11=−48.6946861306418x12=−89.5353906273091x13=−17.2787595947439x14=20.4203522483337x15=−64.4026493985908x16=14.1371669411541x17=−26.7035375555132x18=−70.6858347057703x19=−32.9867228626928x20=4.71238898038469x21=−95.8185759344887x22=−7.85398163397448x23=−23.5619449019235x24=−36.1283155162826x25=−83.2522053201295x26=−1.5707963267949x27=−58.1194640914112x28=−10.9955742875643x29=1.5707963267949x30=29.845130209103x31=−73.8274273593601x32=−92.6769832808989x33=−54.9778714378214x34=−76.9690200129499x35=−1610.06623496477x36=−61.261056745001x37=17.2787595947439x38=10.9955742875643x39=−51.8362787842316x40=−45.553093477052x41=−42.4115008234622x42=−80.1106126665397x43=−29.845130209103x44=−14.1371669411541Las raíces dadas
x35=−1610.06623496477x8=−98.9601685880785x21=−95.8185759344887x32=−92.6769832808989x12=−89.5353906273091x2=−86.3937979737193x25=−83.2522053201295x42=−80.1106126665397x34=−76.9690200129499x31=−73.8274273593601x18=−70.6858347057703x4=−67.5442420521806x15=−64.4026493985908x36=−61.261056745001x27=−58.1194640914112x33=−54.9778714378214x39=−51.8362787842316x11=−48.6946861306418x40=−45.553093477052x41=−42.4115008234622x9=−39.2699081698724x24=−36.1283155162826x19=−32.9867228626928x43=−29.845130209103x17=−26.7035375555132x23=−23.5619449019235x6=−20.4203522483337x13=−17.2787595947439x44=−14.1371669411541x28=−10.9955742875643x22=−7.85398163397448x5=−4.71238898038469x26=−1.5707963267949x7=0.760491357747641x29=1.5707963267949x20=4.71238898038469x1=7.85398163397448x38=10.9955742875643x16=14.1371669411541x37=17.2787595947439x14=20.4203522483337x3=23.5619449019235x10=26.7035375555132x30=29.845130209103son puntos de cambio del signo de desigualdad en las soluciones.
Primero definámonos con el signo hasta el punto extremo izquierdo:
x0<x35Consideremos, por ejemplo, el punto
x0=x35−101=
−1610.06623496477+−101=
−1610.16623496477lo sustituimos en la expresión
((3x+(2x+3))−7)cos(x)>0(−7+(3−1610.16623496477+(2−1610.16623496477+3)))cos(−1610.16623496477)>00.399333666587358 > 0
significa que una de las soluciones de nuestra ecuación será con:
x<−1610.06623496477 _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____
\ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ /
-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------
x35 x8 x21 x32 x12 x2 x25 x42 x34 x31 x18 x4 x15 x36 x27 x33 x39 x11 x40 x41 x9 x24 x19 x43 x17 x23 x6 x13 x44 x28 x22 x5 x26 x7 x29 x20 x1 x38 x16 x37 x14 x3 x10 x30Recibiremos otras soluciones de la desigualdad pasando al polo siguiente etc.
etc.
Respuesta:
x<−1610.06623496477x>−98.9601685880785∧x<−95.8185759344887x>−92.6769832808989∧x<−89.5353906273091x>−86.3937979737193∧x<−83.2522053201295x>−80.1106126665397∧x<−76.9690200129499x>−73.8274273593601∧x<−70.6858347057703x>−67.5442420521806∧x<−64.4026493985908x>−61.261056745001∧x<−58.1194640914112x>−54.9778714378214∧x<−51.8362787842316x>−48.6946861306418∧x<−45.553093477052x>−42.4115008234622∧x<−39.2699081698724x>−36.1283155162826∧x<−32.9867228626928x>−29.845130209103∧x<−26.7035375555132x>−23.5619449019235∧x<−20.4203522483337x>−17.2787595947439∧x<−14.1371669411541x>−10.9955742875643∧x<−7.85398163397448x>−4.71238898038469∧x<−1.5707963267949x>0.760491357747641∧x<1.5707963267949x>4.71238898038469∧x<7.85398163397448x>10.9955742875643∧x<14.1371669411541x>17.2787595947439∧x<20.4203522483337x>23.5619449019235∧x<26.7035375555132x>29.845130209103
-3-5x<=x+3
(x-5,7)*(x-7,2)>0
(x-4)^2/(x-1)>0
x-4x^2/x-1>0