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- La ecuación:
- Ecuación x^2-49=0
-
Ecuación 1-x/2=x/3
-
Ecuación 3*x^2-9=0
-
Ecuación -8x-17=3x-105
- Expresar {x} en función de y en la ecuación:
- 4*x-1*y=-3
- -11*x+9*y=-20
- -19*x+14*y=20
- 5*x-14*y=-15
-
Expresiones idénticas
- ((x^ dos - uno)^ dos / tres - veintiuno / ocho)*((x^ dos - uno)^ dos / cuatro + cinco)- tres = cero
- ((x al cuadrado menos 1) al cuadrado dividir por 3 menos 21 dividir por 8) multiplicar por ((x al cuadrado menos 1) al cuadrado dividir por 4 más 5) menos 3 es igual a 0
- ((x en el grado dos menos uno) en el grado dos dividir por tres menos veintiuno dividir por ocho) multiplicar por ((x en el grado dos menos uno) en el grado dos dividir por cuatro más cinco) menos tres es igual a cero
- ((x2-1)2/3-21/8)*((x2-1)2/4+5)-3=0
- x2-12/3-21/8*x2-12/4+5-3=0
- ((x²-1)²/3-21/8)*((x²-1)²/4+5)-3=0
- ((x en el grado 2-1) en el grado 2/3-21/8)*((x en el grado 2-1) en el grado 2/4+5)-3=0
- ((x^2-1)^2/3-21/8)((x^2-1)^2/4+5)-3=0
- ((x2-1)2/3-21/8)((x2-1)2/4+5)-3=0
- x2-12/3-21/8x2-12/4+5-3=0
- x^2-1^2/3-21/8x^2-1^2/4+5-3=0
- ((x^2-1)^2/3-21/8)*((x^2-1)^2/4+5)-3=O
- ((x^2-1)^2 dividir por 3-21 dividir por 8)*((x^2-1)^2 dividir por 4+5)-3=0
-
Expresiones semejantes
- ((x^2-1)^2/3-21/8)*((x^2+1)^2/4+5)-3=0
- ((x^2-1)^2/3-21/8)*((x^2-1)^2/4-5)-3=0
- ((x^2+1)^2/3-21/8)*((x^2-1)^2/4+5)-3=0
- ((x^2-1)^2/3+21/8)*((x^2-1)^2/4+5)-3=0
- ((x^2-1)^2/3-21/8)*((x^2-1)^2/4+5)+3=0
((x^2-1)^2/3-21/8)*((x^2-1)^2/4+5)-3=0 la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Ha introducido
[src]
/ 2 \ / 2 \ |/ 2 \ | |/ 2 \ | |\x - 1/ 21| |\x - 1/ | |--------- - --|*|--------- + 5| - 3 = 0 \ 3 8 / \ 4 /
$$\left(\frac{\left(x^{2} - 1\right)^{2}}{3} - \frac{21}{8}\right) \left(\frac{\left(x^{2} - 1\right)^{2}}{4} + 5\right) - 3 = 0$$
Suma y producto de raíces
[src]
suma
/ / ________________\\ / / ________________\\ / / ________________\\ / / ________________\\ / / ________________\\ / / ________________\\ / / ________________\\ / / ________________\\
__________________________ __________________________ ___________________________ ___________________________ | | / _______ || | | / _______ || | | / _______ || | | / _______ || | | / _______ || | | / _______ || | | / _______ || | | / _______ ||
/ _________________ / _________________ / _________________ / _________________ _________________ | |\/ 97 + \/ 58945 || _________________ | |\/ 97 + \/ 58945 || _________________ | |\/ 97 + \/ 58945 || _________________ | |\/ 97 + \/ 58945 || _________________ | |\/ 97 + \/ 58945 || _________________ | |\/ 97 + \/ 58945 || _________________ | |\/ 97 + \/ 58945 || _________________ | |\/ 97 + \/ 58945 ||
/ / _______ / / _______ / / _______ / / _______ / _______ |atan|-------------------|| / _______ |atan|-------------------|| / _______ |atan|-------------------|| / _______ |atan|-------------------|| / _______ |atan|-------------------|| / _______ |atan|-------------------|| / _______ |atan|-------------------|| / _______ |atan|-------------------||
/ \/ -97 + \/ 58945 / \/ -97 + \/ 58945 / \/ -97 + \/ 58945 / \/ -97 + \/ 58945 / 113 \/ 58945 | \ 4 /| / 113 \/ 58945 | \ 4 /| / 113 \/ 58945 | \ 4 /| / 113 \/ 58945 | \ 4 /| / 113 \/ 58945 | \ 4 /| / 113 \/ 58945 | \ 4 /| / 113 \/ 58945 | \ 4 /| / 113 \/ 58945 | \ 4 /|
- / 1 + -------------------- + / 1 + -------------------- - I* / -1 + -------------------- + I* / -1 + -------------------- + - 4 / --- + --------- *cos|-------------------------| - I*4 / --- + --------- *sin|-------------------------| + - 4 / --- + --------- *cos|-------------------------| + I*4 / --- + --------- *sin|-------------------------| + 4 / --- + --------- *cos|-------------------------| - I*4 / --- + --------- *sin|-------------------------| + 4 / --- + --------- *cos|-------------------------| + I*4 / --- + --------- *sin|-------------------------|
\/ 4 \/ 4 \/ 4 \/ 4 \/ 16 16 \ 2 / \/ 16 16 \ 2 / \/ 16 16 \ 2 / \/ 16 16 \ 2 / \/ 16 16 \ 2 / \/ 16 16 \ 2 / \/ 16 16 \ 2 / \/ 16 16 \ 2 /
$$\left(\left(\sqrt[4]{\frac{113}{16} + \frac{\sqrt{58945}}{16}} \cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{97 + \sqrt{58945}}}{4} \right)}}{2} \right)} - i \sqrt[4]{\frac{113}{16} + \frac{\sqrt{58945}}{16}} \sin{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{97 + \sqrt{58945}}}{4} \right)}}{2} \right)}\right) + \left(\left(\left(- \sqrt[4]{\frac{113}{16} + \frac{\sqrt{58945}}{16}} \cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{97 + \sqrt{58945}}}{4} \right)}}{2} \right)} - i \sqrt[4]{\frac{113}{16} + \frac{\sqrt{58945}}{16}} \sin{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{97 + \sqrt{58945}}}{4} \right)}}{2} \right)}\right) + \left(\left(\left(- \sqrt{1 + \frac{\sqrt{-97 + \sqrt{58945}}}{4}} + \sqrt{1 + \frac{\sqrt{-97 + \sqrt{58945}}}{4}}\right) - i \sqrt{-1 + \frac{\sqrt{-97 + \sqrt{58945}}}{4}}\right) + i \sqrt{-1 + \frac{\sqrt{-97 + \sqrt{58945}}}{4}}\right)\right) + \left(- \sqrt[4]{\frac{113}{16} + \frac{\sqrt{58945}}{16}} \cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{97 + \sqrt{58945}}}{4} \right)}}{2} \right)} + i \sqrt[4]{\frac{113}{16} + \frac{\sqrt{58945}}{16}} \sin{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{97 + \sqrt{58945}}}{4} \right)}}{2} \right)}\right)\right)\right) + \left(\sqrt[4]{\frac{113}{16} + \frac{\sqrt{58945}}{16}} \cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{97 + \sqrt{58945}}}{4} \right)}}{2} \right)} + i \sqrt[4]{\frac{113}{16} + \frac{\sqrt{58945}}{16}} \sin{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{97 + \sqrt{58945}}}{4} \right)}}{2} \right)}\right)$$
=
0
$$0$$
producto
/ / / ________________\\ / / ________________\\\ / / / ________________\\ / / ________________\\\ / / / ________________\\ / / ________________\\\ / / / ________________\\ / / ________________\\\
__________________________ __________________________ / ___________________________\ ___________________________ | | | / _______ || | | / _______ ||| | | | / _______ || | | / _______ ||| | | | / _______ || | | / _______ ||| | | | / _______ || | | / _______ |||
/ _________________ / _________________ | / _________________ | / _________________ | _________________ | |\/ 97 + \/ 58945 || _________________ | |\/ 97 + \/ 58945 ||| | _________________ | |\/ 97 + \/ 58945 || _________________ | |\/ 97 + \/ 58945 ||| | _________________ | |\/ 97 + \/ 58945 || _________________ | |\/ 97 + \/ 58945 ||| | _________________ | |\/ 97 + \/ 58945 || _________________ | |\/ 97 + \/ 58945 |||
/ / _______ / / _______ | / / _______ | / / _______ | / _______ |atan|-------------------|| / _______ |atan|-------------------||| | / _______ |atan|-------------------|| / _______ |atan|-------------------||| | / _______ |atan|-------------------|| / _______ |atan|-------------------||| | / _______ |atan|-------------------|| / _______ |atan|-------------------|||
/ \/ -97 + \/ 58945 / \/ -97 + \/ 58945 | / \/ -97 + \/ 58945 | / \/ -97 + \/ 58945 | / 113 \/ 58945 | \ 4 /| / 113 \/ 58945 | \ 4 /|| | / 113 \/ 58945 | \ 4 /| / 113 \/ 58945 | \ 4 /|| | / 113 \/ 58945 | \ 4 /| / 113 \/ 58945 | \ 4 /|| | / 113 \/ 58945 | \ 4 /| / 113 \/ 58945 | \ 4 /||
- / 1 + -------------------- * / 1 + -------------------- *|-I* / -1 + -------------------- |*I* / -1 + -------------------- *|- 4 / --- + --------- *cos|-------------------------| - I*4 / --- + --------- *sin|-------------------------||*|- 4 / --- + --------- *cos|-------------------------| + I*4 / --- + --------- *sin|-------------------------||*|4 / --- + --------- *cos|-------------------------| - I*4 / --- + --------- *sin|-------------------------||*|4 / --- + --------- *cos|-------------------------| + I*4 / --- + --------- *sin|-------------------------||
\/ 4 \/ 4 \ \/ 4 / \/ 4 \ \/ 16 16 \ 2 / \/ 16 16 \ 2 // \ \/ 16 16 \ 2 / \/ 16 16 \ 2 // \\/ 16 16 \ 2 / \/ 16 16 \ 2 // \\/ 16 16 \ 2 / \/ 16 16 \ 2 //
$$i \sqrt{-1 + \frac{\sqrt{-97 + \sqrt{58945}}}{4}} \cdot - i \sqrt{-1 + \frac{\sqrt{-97 + \sqrt{58945}}}{4}} \cdot - \sqrt{1 + \frac{\sqrt{-97 + \sqrt{58945}}}{4}} \sqrt{1 + \frac{\sqrt{-97 + \sqrt{58945}}}{4}} \left(- \sqrt[4]{\frac{113}{16} + \frac{\sqrt{58945}}{16}} \cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{97 + \sqrt{58945}}}{4} \right)}}{2} \right)} - i \sqrt[4]{\frac{113}{16} + \frac{\sqrt{58945}}{16}} \sin{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{97 + \sqrt{58945}}}{4} \right)}}{2} \right)}\right) \left(- \sqrt[4]{\frac{113}{16} + \frac{\sqrt{58945}}{16}} \cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{97 + \sqrt{58945}}}{4} \right)}}{2} \right)} + i \sqrt[4]{\frac{113}{16} + \frac{\sqrt{58945}}{16}} \sin{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{97 + \sqrt{58945}}}{4} \right)}}{2} \right)}\right) \left(\sqrt[4]{\frac{113}{16} + \frac{\sqrt{58945}}{16}} \cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{97 + \sqrt{58945}}}{4} \right)}}{2} \right)} - i \sqrt[4]{\frac{113}{16} + \frac{\sqrt{58945}}{16}} \sin{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{97 + \sqrt{58945}}}{4} \right)}}{2} \right)}\right) \left(\sqrt[4]{\frac{113}{16} + \frac{\sqrt{58945}}{16}} \cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{97 + \sqrt{58945}}}{4} \right)}}{2} \right)} + i \sqrt[4]{\frac{113}{16} + \frac{\sqrt{58945}}{16}} \sin{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{97 + \sqrt{58945}}}{4} \right)}}{2} \right)}\right)$$
=
-1443/8
$$- \frac{1443}{8}$$
-1443/8
Respuesta rápida
[src]
__________________________
/ _________________
/ / _______
/ \/ -97 + \/ 58945
x1 = - / 1 + --------------------
\/ 4
$$x_{1} = - \sqrt{1 + \frac{\sqrt{-97 + \sqrt{58945}}}{4}}$$
__________________________
/ _________________
/ / _______
/ \/ -97 + \/ 58945
x2 = / 1 + --------------------
\/ 4
$$x_{2} = \sqrt{1 + \frac{\sqrt{-97 + \sqrt{58945}}}{4}}$$
___________________________
/ _________________
/ / _______
/ \/ -97 + \/ 58945
x3 = -I* / -1 + --------------------
\/ 4
$$x_{3} = - i \sqrt{-1 + \frac{\sqrt{-97 + \sqrt{58945}}}{4}}$$
___________________________
/ _________________
/ / _______
/ \/ -97 + \/ 58945
x4 = I* / -1 + --------------------
\/ 4
$$x_{4} = i \sqrt{-1 + \frac{\sqrt{-97 + \sqrt{58945}}}{4}}$$
/ / ________________\\ / / ________________\\
| | / _______ || | | / _______ ||
_________________ | |\/ 97 + \/ 58945 || _________________ | |\/ 97 + \/ 58945 ||
/ _______ |atan|-------------------|| / _______ |atan|-------------------||
/ 113 \/ 58945 | \ 4 /| / 113 \/ 58945 | \ 4 /|
x5 = - 4 / --- + --------- *cos|-------------------------| - I*4 / --- + --------- *sin|-------------------------|
\/ 16 16 \ 2 / \/ 16 16 \ 2 /
$$x_{5} = - \sqrt[4]{\frac{113}{16} + \frac{\sqrt{58945}}{16}} \cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{97 + \sqrt{58945}}}{4} \right)}}{2} \right)} - i \sqrt[4]{\frac{113}{16} + \frac{\sqrt{58945}}{16}} \sin{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{97 + \sqrt{58945}}}{4} \right)}}{2} \right)}$$
/ / ________________\\ / / ________________\\
| | / _______ || | | / _______ ||
_________________ | |\/ 97 + \/ 58945 || _________________ | |\/ 97 + \/ 58945 ||
/ _______ |atan|-------------------|| / _______ |atan|-------------------||
/ 113 \/ 58945 | \ 4 /| / 113 \/ 58945 | \ 4 /|
x6 = - 4 / --- + --------- *cos|-------------------------| + I*4 / --- + --------- *sin|-------------------------|
\/ 16 16 \ 2 / \/ 16 16 \ 2 /
$$x_{6} = - \sqrt[4]{\frac{113}{16} + \frac{\sqrt{58945}}{16}} \cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{97 + \sqrt{58945}}}{4} \right)}}{2} \right)} + i \sqrt[4]{\frac{113}{16} + \frac{\sqrt{58945}}{16}} \sin{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{97 + \sqrt{58945}}}{4} \right)}}{2} \right)}$$
/ / ________________\\ / / ________________\\
| | / _______ || | | / _______ ||
_________________ | |\/ 97 + \/ 58945 || _________________ | |\/ 97 + \/ 58945 ||
/ _______ |atan|-------------------|| / _______ |atan|-------------------||
/ 113 \/ 58945 | \ 4 /| / 113 \/ 58945 | \ 4 /|
x7 = 4 / --- + --------- *cos|-------------------------| - I*4 / --- + --------- *sin|-------------------------|
\/ 16 16 \ 2 / \/ 16 16 \ 2 /
$$x_{7} = \sqrt[4]{\frac{113}{16} + \frac{\sqrt{58945}}{16}} \cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{97 + \sqrt{58945}}}{4} \right)}}{2} \right)} - i \sqrt[4]{\frac{113}{16} + \frac{\sqrt{58945}}{16}} \sin{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{97 + \sqrt{58945}}}{4} \right)}}{2} \right)}$$
/ / ________________\\ / / ________________\\
| | / _______ || | | / _______ ||
_________________ | |\/ 97 + \/ 58945 || _________________ | |\/ 97 + \/ 58945 ||
/ _______ |atan|-------------------|| / _______ |atan|-------------------||
/ 113 \/ 58945 | \ 4 /| / 113 \/ 58945 | \ 4 /|
x8 = 4 / --- + --------- *cos|-------------------------| + I*4 / --- + --------- *sin|-------------------------|
\/ 16 16 \ 2 / \/ 16 16 \ 2 /
$$x_{8} = \sqrt[4]{\frac{113}{16} + \frac{\sqrt{58945}}{16}} \cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{97 + \sqrt{58945}}}{4} \right)}}{2} \right)} + i \sqrt[4]{\frac{113}{16} + \frac{\sqrt{58945}}{16}} \sin{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{97 + \sqrt{58945}}}{4} \right)}}{2} \right)}$$
x8 = (113/16 + sqrt(58945)/16)^(1/4)*cos(atan(sqrt(97 + sqrt(58945))/4)/2) + i*(113/16 + sqrt(58945)/16)^(1/4)*sin(atan(sqrt(97 + sqrt(58945))/4)/2)
Respuesta numérica
[src]
x1 = 2.00463112434668
x2 = 1.69049874819781 - 1.36300624270704*i
x3 = 1.69049874819781 + 1.36300624270704*i
x4 = -1.4207554133979*i
x5 = -1.69049874819781 - 1.36300624270704*i
x6 = -2.00463112434668
x7 = -1.69049874819781 + 1.36300624270704*i
x8 = 1.4207554133979*i
x8 = 1.4207554133979*i