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La ecuación:
Ecuación 3^x=27
Ecuación 2x^2-x-1=x^2-5x-(-1-x^2)
Ecuación x(x^2+2x+1)=6(x+1)
Ecuación 4x+1=-3x+15
Expresar {x} en función de y en la ecuación:
-6*x-20*y=8
7*x-1*y=0
2*x-8*y=4
2*x-15*y=-1
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

Simplificar

Gráfica

Trazar el gráfico f1(x)

Trazar el gráfico f2(x)

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

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Expresiones idénticas

Expresiones semejantes

(1+h1)^4*(1+h1/1,5)^4-1,21=0 la ecuación

Solución numérica:

Solución