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- La ecuación:
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Ecuación 8*x=2
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Ecuación 3^x=81
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Ecuación 5x+15=x-1
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Ecuación x^2=12
- Expresar {x} en función de y en la ecuación:
- 4*x-1*y=-3
- -11*x+9*y=-20
- 9*x+17*y=13
- -17*x+2*y=9
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Expresiones idénticas
- (uno +h uno)^ cuatro *(uno +h uno /1, cinco)^ cuatro -1, veintiuno = cero
- (1 más h1) en el grado 4 multiplicar por (1 más h1 dividir por 1,5) en el grado 4 menos 1,21 es igual a 0
- (uno más h uno) en el grado cuatro multiplicar por (uno más h uno dividir por 1, cinco) en el grado cuatro menos 1, veintiuno es igual a cero
- (1+h1)4*(1+h1/1,5)4-1,21=0
- 1+h14*1+h1/1,54-1,21=0
- (1+h1)⁴*(1+h1/1,5)⁴-1,21=0
- (1+h1)^4(1+h1/1,5)^4-1,21=0
- (1+h1)4(1+h1/1,5)4-1,21=0
- 1+h141+h1/1,54-1,21=0
- 1+h1^41+h1/1,5^4-1,21=0
- (1+h1)^4*(1+h1/1,5)^4-1,21=O
- (1+h1)^4*(1+h1 dividir por 1,5)^4-1,21=0
-
Expresiones semejantes
- (1+h1)^4*(1+h1/1,5)^4+1,21=0
- (1-h1)^4*(1+h1/1,5)^4-1,21=0
- (1+h1)^4*(1-h1/1,5)^4-1,21=0
(1+h1)^4*(1+h1/1,5)^4-1,21=0 la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Ha introducido
[src]
4
4 / h1\ 121
(1 + h1) *|1 + ---| - --- = 0
\ 3/2/ 100
$$\left(h_{1} + 1\right)^{4} \left(\frac{h_{1}}{\frac{3}{2}} + 1\right)^{4} - \frac{121}{100} = 0$$
Suma y producto de raíces
[src]
suma
/ / _____\\ / / _____\\ / / _____\\ / / _____\\ / / _____\\ / / _____\\ / / _____\\ / / _____\\
| |12*\/ 110 || | |12*\/ 110 || | |12*\/ 110 || | |12*\/ 110 || | |12*\/ 110 || | |12*\/ 110 || | |12*\/ 110 || | |12*\/ 110 ||
|atan|----------|| |atan|----------|| |atan|----------|| |atan|----------|| |atan|----------|| |atan|----------|| |atan|----------|| |atan|----------||
________________ 3/4 4 ______ | \ 5 /| 3/4 4 ______ | \ 5 /| 3/4 4 ______ | \ 5 /| 3/4 4 ______ | \ 5 /| 3/4 4 ______ | \ 5 /| 3/4 4 ______ | \ 5 /| 3/4 4 ______ | \ 5 /| 3/4 4 ______ | \ 5 /| ________________ __________________ __________________
/ _____ 5 *\/ 3173 *cos|----------------| I*5 *\/ 3173 *sin|----------------| 5 *\/ 3173 *cos|----------------| I*5 *\/ 3173 *sin|----------------| 5 *\/ 3173 *cos|----------------| I*5 *\/ 3173 *sin|----------------| 5 *\/ 3173 *cos|----------------| I*5 *\/ 3173 *sin|----------------| / _____ / _____ / _____
5 / 1 3*\/ 110 5 \ 2 / \ 2 / 5 \ 2 / \ 2 / 5 \ 2 / \ 2 / 5 \ 2 / \ 2 / 5 / 1 3*\/ 110 5 / 1 3*\/ 110 5 / 1 3*\/ 110
- - + / -- + --------- + - - - ----------------------------------- + ------------------------------------- + - - + ----------------------------------- - ------------------------------------- + - - - ----------------------------------- - ------------------------------------- + - - + ----------------------------------- + ------------------------------------- + - - - / -- + --------- + - - - I* / - -- + --------- + - - + I* / - -- + ---------
4 \/ 16 20 4 20 20 4 20 20 4 20 20 4 20 20 4 \/ 16 20 4 \/ 16 20 4 \/ 16 20
$$\left(\left(- \frac{5}{4} - i \sqrt{- \frac{1}{16} + \frac{3 \sqrt{110}}{20}}\right) + \left(\left(- \sqrt{\frac{1}{16} + \frac{3 \sqrt{110}}{20}} - \frac{5}{4}\right) + \left(\left(\left(- \frac{5}{4} - \frac{\sqrt[4]{3173} \cdot 5^{\frac{3}{4}} \cos{\left(\frac{\operatorname{atan}{\left(\frac{12 \sqrt{110}}{5} \right)}}{2} \right)}}{20} - \frac{\sqrt[4]{3173} \cdot 5^{\frac{3}{4}} i \sin{\left(\frac{\operatorname{atan}{\left(\frac{12 \sqrt{110}}{5} \right)}}{2} \right)}}{20}\right) + \left(\left(- \frac{5}{4} + \frac{\sqrt[4]{3173} \cdot 5^{\frac{3}{4}} \cos{\left(\frac{\operatorname{atan}{\left(\frac{12 \sqrt{110}}{5} \right)}}{2} \right)}}{20} - \frac{\sqrt[4]{3173} \cdot 5^{\frac{3}{4}} i \sin{\left(\frac{\operatorname{atan}{\left(\frac{12 \sqrt{110}}{5} \right)}}{2} \right)}}{20}\right) + \left(\left(- \frac{5}{4} + \sqrt{\frac{1}{16} + \frac{3 \sqrt{110}}{20}}\right) + \left(- \frac{5}{4} - \frac{\sqrt[4]{3173} \cdot 5^{\frac{3}{4}} \cos{\left(\frac{\operatorname{atan}{\left(\frac{12 \sqrt{110}}{5} \right)}}{2} \right)}}{20} + \frac{\sqrt[4]{3173} \cdot 5^{\frac{3}{4}} i \sin{\left(\frac{\operatorname{atan}{\left(\frac{12 \sqrt{110}}{5} \right)}}{2} \right)}}{20}\right)\right)\right)\right) + \left(- \frac{5}{4} + \frac{\sqrt[4]{3173} \cdot 5^{\frac{3}{4}} \cos{\left(\frac{\operatorname{atan}{\left(\frac{12 \sqrt{110}}{5} \right)}}{2} \right)}}{20} + \frac{\sqrt[4]{3173} \cdot 5^{\frac{3}{4}} i \sin{\left(\frac{\operatorname{atan}{\left(\frac{12 \sqrt{110}}{5} \right)}}{2} \right)}}{20}\right)\right)\right)\right) + \left(- \frac{5}{4} + i \sqrt{- \frac{1}{16} + \frac{3 \sqrt{110}}{20}}\right)$$
=
-10
$$-10$$
producto
/ / / _____\\ / / _____\\\ / / / _____\\ / / _____\\\ / / / _____\\ / / _____\\\ / / / _____\\ / / _____\\\
| | |12*\/ 110 || | |12*\/ 110 ||| | | |12*\/ 110 || | |12*\/ 110 ||| | | |12*\/ 110 || | |12*\/ 110 ||| | | |12*\/ 110 || | |12*\/ 110 |||
| |atan|----------|| |atan|----------||| | |atan|----------|| |atan|----------||| | |atan|----------|| |atan|----------||| | |atan|----------|| |atan|----------|||
/ ________________\ | 3/4 4 ______ | \ 5 /| 3/4 4 ______ | \ 5 /|| | 3/4 4 ______ | \ 5 /| 3/4 4 ______ | \ 5 /|| | 3/4 4 ______ | \ 5 /| 3/4 4 ______ | \ 5 /|| | 3/4 4 ______ | \ 5 /| 3/4 4 ______ | \ 5 /|| / ________________\ / __________________\ / __________________\
| / _____ | | 5 *\/ 3173 *cos|----------------| I*5 *\/ 3173 *sin|----------------|| | 5 *\/ 3173 *cos|----------------| I*5 *\/ 3173 *sin|----------------|| | 5 *\/ 3173 *cos|----------------| I*5 *\/ 3173 *sin|----------------|| | 5 *\/ 3173 *cos|----------------| I*5 *\/ 3173 *sin|----------------|| | / _____ | | / _____ | | / _____ |
| 5 / 1 3*\/ 110 | | 5 \ 2 / \ 2 /| | 5 \ 2 / \ 2 /| | 5 \ 2 / \ 2 /| | 5 \ 2 / \ 2 /| | 5 / 1 3*\/ 110 | | 5 / 1 3*\/ 110 | | 5 / 1 3*\/ 110 |
|- - + / -- + --------- |*|- - - ----------------------------------- + -------------------------------------|*|- - + ----------------------------------- - -------------------------------------|*|- - - ----------------------------------- - -------------------------------------|*|- - + ----------------------------------- + -------------------------------------|*|- - - / -- + --------- |*|- - - I* / - -- + --------- |*|- - + I* / - -- + --------- |
\ 4 \/ 16 20 / \ 4 20 20 / \ 4 20 20 / \ 4 20 20 / \ 4 20 20 / \ 4 \/ 16 20 / \ 4 \/ 16 20 / \ 4 \/ 16 20 /
$$\left(- \frac{5}{4} + \sqrt{\frac{1}{16} + \frac{3 \sqrt{110}}{20}}\right) \left(- \frac{5}{4} - \frac{\sqrt[4]{3173} \cdot 5^{\frac{3}{4}} \cos{\left(\frac{\operatorname{atan}{\left(\frac{12 \sqrt{110}}{5} \right)}}{2} \right)}}{20} + \frac{\sqrt[4]{3173} \cdot 5^{\frac{3}{4}} i \sin{\left(\frac{\operatorname{atan}{\left(\frac{12 \sqrt{110}}{5} \right)}}{2} \right)}}{20}\right) \left(- \frac{5}{4} + \frac{\sqrt[4]{3173} \cdot 5^{\frac{3}{4}} \cos{\left(\frac{\operatorname{atan}{\left(\frac{12 \sqrt{110}}{5} \right)}}{2} \right)}}{20} - \frac{\sqrt[4]{3173} \cdot 5^{\frac{3}{4}} i \sin{\left(\frac{\operatorname{atan}{\left(\frac{12 \sqrt{110}}{5} \right)}}{2} \right)}}{20}\right) \left(- \frac{5}{4} - \frac{\sqrt[4]{3173} \cdot 5^{\frac{3}{4}} \cos{\left(\frac{\operatorname{atan}{\left(\frac{12 \sqrt{110}}{5} \right)}}{2} \right)}}{20} - \frac{\sqrt[4]{3173} \cdot 5^{\frac{3}{4}} i \sin{\left(\frac{\operatorname{atan}{\left(\frac{12 \sqrt{110}}{5} \right)}}{2} \right)}}{20}\right) \left(- \frac{5}{4} + \frac{\sqrt[4]{3173} \cdot 5^{\frac{3}{4}} \cos{\left(\frac{\operatorname{atan}{\left(\frac{12 \sqrt{110}}{5} \right)}}{2} \right)}}{20} + \frac{\sqrt[4]{3173} \cdot 5^{\frac{3}{4}} i \sin{\left(\frac{\operatorname{atan}{\left(\frac{12 \sqrt{110}}{5} \right)}}{2} \right)}}{20}\right) \left(- \sqrt{\frac{1}{16} + \frac{3 \sqrt{110}}{20}} - \frac{5}{4}\right) \left(- \frac{5}{4} - i \sqrt{- \frac{1}{16} + \frac{3 \sqrt{110}}{20}}\right) \left(- \frac{5}{4} + i \sqrt{- \frac{1}{16} + \frac{3 \sqrt{110}}{20}}\right)$$
=
-1701 ------ 1600
$$- \frac{1701}{1600}$$
-1701/1600
Respuesta rápida
[src]
________________
/ _____
5 / 1 3*\/ 110
h11 = - - + / -- + ---------
4 \/ 16 20
$$h_{11} = - \frac{5}{4} + \sqrt{\frac{1}{16} + \frac{3 \sqrt{110}}{20}}$$
/ / _____\\ / / _____\\
| |12*\/ 110 || | |12*\/ 110 ||
|atan|----------|| |atan|----------||
3/4 4 ______ | \ 5 /| 3/4 4 ______ | \ 5 /|
5 *\/ 3173 *cos|----------------| I*5 *\/ 3173 *sin|----------------|
5 \ 2 / \ 2 /
h12 = - - - ----------------------------------- + -------------------------------------
4 20 20
$$h_{12} = - \frac{5}{4} - \frac{\sqrt[4]{3173} \cdot 5^{\frac{3}{4}} \cos{\left(\frac{\operatorname{atan}{\left(\frac{12 \sqrt{110}}{5} \right)}}{2} \right)}}{20} + \frac{\sqrt[4]{3173} \cdot 5^{\frac{3}{4}} i \sin{\left(\frac{\operatorname{atan}{\left(\frac{12 \sqrt{110}}{5} \right)}}{2} \right)}}{20}$$
/ / _____\\ / / _____\\
| |12*\/ 110 || | |12*\/ 110 ||
|atan|----------|| |atan|----------||
3/4 4 ______ | \ 5 /| 3/4 4 ______ | \ 5 /|
5 *\/ 3173 *cos|----------------| I*5 *\/ 3173 *sin|----------------|
5 \ 2 / \ 2 /
h13 = - - + ----------------------------------- - -------------------------------------
4 20 20
$$h_{13} = - \frac{5}{4} + \frac{\sqrt[4]{3173} \cdot 5^{\frac{3}{4}} \cos{\left(\frac{\operatorname{atan}{\left(\frac{12 \sqrt{110}}{5} \right)}}{2} \right)}}{20} - \frac{\sqrt[4]{3173} \cdot 5^{\frac{3}{4}} i \sin{\left(\frac{\operatorname{atan}{\left(\frac{12 \sqrt{110}}{5} \right)}}{2} \right)}}{20}$$
/ / _____\\ / / _____\\
| |12*\/ 110 || | |12*\/ 110 ||
|atan|----------|| |atan|----------||
3/4 4 ______ | \ 5 /| 3/4 4 ______ | \ 5 /|
5 *\/ 3173 *cos|----------------| I*5 *\/ 3173 *sin|----------------|
5 \ 2 / \ 2 /
h14 = - - - ----------------------------------- - -------------------------------------
4 20 20
$$h_{14} = - \frac{5}{4} - \frac{\sqrt[4]{3173} \cdot 5^{\frac{3}{4}} \cos{\left(\frac{\operatorname{atan}{\left(\frac{12 \sqrt{110}}{5} \right)}}{2} \right)}}{20} - \frac{\sqrt[4]{3173} \cdot 5^{\frac{3}{4}} i \sin{\left(\frac{\operatorname{atan}{\left(\frac{12 \sqrt{110}}{5} \right)}}{2} \right)}}{20}$$
/ / _____\\ / / _____\\
| |12*\/ 110 || | |12*\/ 110 ||
|atan|----------|| |atan|----------||
3/4 4 ______ | \ 5 /| 3/4 4 ______ | \ 5 /|
5 *\/ 3173 *cos|----------------| I*5 *\/ 3173 *sin|----------------|
5 \ 2 / \ 2 /
h15 = - - + ----------------------------------- + -------------------------------------
4 20 20
$$h_{15} = - \frac{5}{4} + \frac{\sqrt[4]{3173} \cdot 5^{\frac{3}{4}} \cos{\left(\frac{\operatorname{atan}{\left(\frac{12 \sqrt{110}}{5} \right)}}{2} \right)}}{20} + \frac{\sqrt[4]{3173} \cdot 5^{\frac{3}{4}} i \sin{\left(\frac{\operatorname{atan}{\left(\frac{12 \sqrt{110}}{5} \right)}}{2} \right)}}{20}$$
________________
/ _____
5 / 1 3*\/ 110
h16 = - - - / -- + ---------
4 \/ 16 20
$$h_{16} = - \sqrt{\frac{1}{16} + \frac{3 \sqrt{110}}{20}} - \frac{5}{4}$$
__________________
/ _____
5 / 1 3*\/ 110
h17 = - - - I* / - -- + ---------
4 \/ 16 20
$$h_{17} = - \frac{5}{4} - i \sqrt{- \frac{1}{16} + \frac{3 \sqrt{110}}{20}}$$
__________________
/ _____
5 / 1 3*\/ 110
h18 = - - + I* / - -- + ---------
4 \/ 16 20
$$h_{18} = - \frac{5}{4} + i \sqrt{- \frac{1}{16} + \frac{3 \sqrt{110}}{20}}$$
h18 = -5/4 + i*sqrt(-1/16 + 3*sqrt(110)/20)
Respuesta numérica
[src]
h11 = -2.52895006636507
h12 = -1.25 - 1.22911076484393*i
h13 = -2.15469726166633 - 0.869469456201058*i
h14 = -0.345302738333666 + 0.869469456201058*i
h15 = -0.345302738333666 - 0.869469456201058*i
h16 = -1.25 + 1.22911076484393*i
h17 = 0.0289500663650741
h18 = -2.15469726166633 + 0.869469456201058*i
h18 = -2.15469726166633 + 0.869469456201058*i