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- La ecuación:
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Ecuación (8/2)^(x+8)=6^x
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Ecuación 2+x=6
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Ecuación 2x(x-8)=-18-x
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Ecuación x^3-3*x^2-4*x+12=0
- Expresar {x} en función de y en la ecuación:
- 9*x+7*y=4
- 18*x-7*y=5
- 13*x-1*y=5
- -1*x+11*y=16
- Derivada de:
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√x^2-1
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Expresiones idénticas
- √x^ dos - uno =(x+ siete)(√x+ uno /√x- uno)
- √x al cuadrado menos 1 es igual a (x más 7)(√x más 1 dividir por √x menos 1)
- √x en el grado dos menos uno es igual a (x más siete)(√x más uno dividir por √x menos uno)
- √x2-1=(x+7)(√x+1/√x-1)
- √x2-1=x+7√x+1/√x-1
- √x²-1=(x+7)(√x+1/√x-1)
- √x en el grado 2-1=(x+7)(√x+1/√x-1)
- √x^2-1=x+7√x+1/√x-1
- √x^2-1=(x+7)(√x+1 dividir por √x-1)
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Expresiones semejantes
- √x^2-1=(x+7)(√x-1/√x-1)
- √x^2-1=(x+7)(√x+1/√x+1)
- √x^2-1=(x-7)(√x+1/√x-1)
- √x^2+1=(x+7)(√x+1/√x-1)
√x^2-1=(x+7)(√x+1/√x-1) la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Ha introducido
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2
___ / ___ 1 \
\/ x - 1 = (x + 7)*|\/ x + ----- - 1|
| ___ |
\ \/ x /
$$\left(\sqrt{x}\right)^{2} - 1 = \left(x + 7\right) \left(\left(\sqrt{x} + \frac{1}{\sqrt{x}}\right) - 1\right)$$
Respuesta rápida
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_________________________________________________________________________________________________________________________________
/ ___________________
/ / _____
/ 64 / 64*I*\/ 111 128
I* / - ------------------------------------------------------------------- + 2*3 / 64 + ------------ + --------------------------
_________________________________________________________ / _________________________________________________________ \/ 9 ___________________
/ ___________________ / / ___________________ / _____
/ / _____ / / / _____ / 64*I*\/ 111
/ / 64*I*\/ 111 128 / / / 64*I*\/ 111 128 3*3 / 64 + ------------
/ 2*3 / 64 + ------------ + -------------------------- / / 2*3 / 64 + ------------ + -------------------------- \/ 9
/ \/ 9 ___________________ / / \/ 9 ___________________
/ / _____ / / / _____
/ / 64*I*\/ 111 / / / 64*I*\/ 111
/ 3*3 / 64 + ------------ / / 3*3 / 64 + ------------
\/ \/ 9 \/ \/ \/ 9
x1 = -3 + ------------------------------------------------------------------- - --------------------------------------------------------------------------------------------------------------------------------------------------
2 2
$$x_{1} = -3 - \frac{i \sqrt{\frac{128}{3 \sqrt[3]{64 + \frac{64 \sqrt{111} i}{9}}} - \frac{64}{\sqrt{\frac{128}{3 \sqrt[3]{64 + \frac{64 \sqrt{111} i}{9}}} + 2 \sqrt[3]{64 + \frac{64 \sqrt{111} i}{9}}}} + 2 \sqrt[3]{64 + \frac{64 \sqrt{111} i}{9}}}}{2} + \frac{\sqrt{\frac{128}{3 \sqrt[3]{64 + \frac{64 \sqrt{111} i}{9}}} + 2 \sqrt[3]{64 + \frac{64 \sqrt{111} i}{9}}}}{2}$$
_________________________________________________________________________________________________________________________________
/ ___________________
/ / _____
/ 64 / 64*I*\/ 111 128
I* / - ------------------------------------------------------------------- + 2*3 / 64 + ------------ + --------------------------
_________________________________________________________ / _________________________________________________________ \/ 9 ___________________
/ ___________________ / / ___________________ / _____
/ / _____ / / / _____ / 64*I*\/ 111
/ / 64*I*\/ 111 128 / / / 64*I*\/ 111 128 3*3 / 64 + ------------
/ 2*3 / 64 + ------------ + -------------------------- / / 2*3 / 64 + ------------ + -------------------------- \/ 9
/ \/ 9 ___________________ / / \/ 9 ___________________
/ / _____ / / / _____
/ / 64*I*\/ 111 / / / 64*I*\/ 111
/ 3*3 / 64 + ------------ / / 3*3 / 64 + ------------
\/ \/ 9 \/ \/ \/ 9
x2 = -3 + ------------------------------------------------------------------- + --------------------------------------------------------------------------------------------------------------------------------------------------
2 2
$$x_{2} = -3 + \frac{\sqrt{\frac{128}{3 \sqrt[3]{64 + \frac{64 \sqrt{111} i}{9}}} + 2 \sqrt[3]{64 + \frac{64 \sqrt{111} i}{9}}}}{2} + \frac{i \sqrt{\frac{128}{3 \sqrt[3]{64 + \frac{64 \sqrt{111} i}{9}}} - \frac{64}{\sqrt{\frac{128}{3 \sqrt[3]{64 + \frac{64 \sqrt{111} i}{9}}} + 2 \sqrt[3]{64 + \frac{64 \sqrt{111} i}{9}}}} + 2 \sqrt[3]{64 + \frac{64 \sqrt{111} i}{9}}}}{2}$$
x2 = -3 + sqrt(128/(3*(64 + 64*sqrt(111)*i/9)^(1/3)) + 2*(64 + 64*sqrt(111)*i/9)^(1/3))/2 + i*sqrt(128/(3*(64 + 64*sqrt(111)*i/9)^(1/3)) - 64/sqrt(128/(3*(64 + 64*sqrt(111)*i/9)^(1/3)) + 2*(64 + 64*sqrt(111)*i/9)^(1/3)) + 2*(64 + 64*sqrt(111)*i/9)^(1/3))/2
Suma y producto de raíces
[src]
suma
_________________________________________________________________________________________________________________________________ _________________________________________________________________________________________________________________________________
/ ___________________ / ___________________
/ / _____ / / _____
/ 64 / 64*I*\/ 111 128 / 64 / 64*I*\/ 111 128
I* / - ------------------------------------------------------------------- + 2*3 / 64 + ------------ + -------------------------- I* / - ------------------------------------------------------------------- + 2*3 / 64 + ------------ + --------------------------
_________________________________________________________ / _________________________________________________________ \/ 9 ___________________ _________________________________________________________ / _________________________________________________________ \/ 9 ___________________
/ ___________________ / / ___________________ / _____ / ___________________ / / ___________________ / _____
/ / _____ / / / _____ / 64*I*\/ 111 / / _____ / / / _____ / 64*I*\/ 111
/ / 64*I*\/ 111 128 / / / 64*I*\/ 111 128 3*3 / 64 + ------------ / / 64*I*\/ 111 128 / / / 64*I*\/ 111 128 3*3 / 64 + ------------
/ 2*3 / 64 + ------------ + -------------------------- / / 2*3 / 64 + ------------ + -------------------------- \/ 9 / 2*3 / 64 + ------------ + -------------------------- / / 2*3 / 64 + ------------ + -------------------------- \/ 9
/ \/ 9 ___________________ / / \/ 9 ___________________ / \/ 9 ___________________ / / \/ 9 ___________________
/ / _____ / / / _____ / / _____ / / / _____
/ / 64*I*\/ 111 / / / 64*I*\/ 111 / / 64*I*\/ 111 / / / 64*I*\/ 111
/ 3*3 / 64 + ------------ / / 3*3 / 64 + ------------ / 3*3 / 64 + ------------ / / 3*3 / 64 + ------------
\/ \/ 9 \/ \/ \/ 9 \/ \/ 9 \/ \/ \/ 9
-3 + ------------------------------------------------------------------- - -------------------------------------------------------------------------------------------------------------------------------------------------- + -3 + ------------------------------------------------------------------- + --------------------------------------------------------------------------------------------------------------------------------------------------
2 2 2 2
$$\left(-3 - \frac{i \sqrt{\frac{128}{3 \sqrt[3]{64 + \frac{64 \sqrt{111} i}{9}}} - \frac{64}{\sqrt{\frac{128}{3 \sqrt[3]{64 + \frac{64 \sqrt{111} i}{9}}} + 2 \sqrt[3]{64 + \frac{64 \sqrt{111} i}{9}}}} + 2 \sqrt[3]{64 + \frac{64 \sqrt{111} i}{9}}}}{2} + \frac{\sqrt{\frac{128}{3 \sqrt[3]{64 + \frac{64 \sqrt{111} i}{9}}} + 2 \sqrt[3]{64 + \frac{64 \sqrt{111} i}{9}}}}{2}\right) + \left(-3 + \frac{\sqrt{\frac{128}{3 \sqrt[3]{64 + \frac{64 \sqrt{111} i}{9}}} + 2 \sqrt[3]{64 + \frac{64 \sqrt{111} i}{9}}}}{2} + \frac{i \sqrt{\frac{128}{3 \sqrt[3]{64 + \frac{64 \sqrt{111} i}{9}}} - \frac{64}{\sqrt{\frac{128}{3 \sqrt[3]{64 + \frac{64 \sqrt{111} i}{9}}} + 2 \sqrt[3]{64 + \frac{64 \sqrt{111} i}{9}}}} + 2 \sqrt[3]{64 + \frac{64 \sqrt{111} i}{9}}}}{2}\right)$$
=
_________________________________________________________
/ ___________________
/ / _____
/ / 64*I*\/ 111 128
-6 + / 2*3 / 64 + ------------ + --------------------------
/ \/ 9 ___________________
/ / _____
/ / 64*I*\/ 111
/ 3*3 / 64 + ------------
\/ \/ 9
$$-6 + \sqrt{\frac{128}{3 \sqrt[3]{64 + \frac{64 \sqrt{111} i}{9}}} + 2 \sqrt[3]{64 + \frac{64 \sqrt{111} i}{9}}}$$
producto
/ _________________________________________________________________________________________________________________________________\ / _________________________________________________________________________________________________________________________________\ | / ___________________ | | / ___________________ | | / / _____ | | / / _____ | | / 64 / 64*I*\/ 111 128 | | / 64 / 64*I*\/ 111 128 | | I* / - ------------------------------------------------------------------- + 2*3 / 64 + ------------ + -------------------------- | | I* / - ------------------------------------------------------------------- + 2*3 / 64 + ------------ + -------------------------- | | _________________________________________________________ / _________________________________________________________ \/ 9 ___________________ | | _________________________________________________________ / _________________________________________________________ \/ 9 ___________________ | | / ___________________ / / ___________________ / _____ | | / ___________________ / / ___________________ / _____ | | / / _____ / / / _____ / 64*I*\/ 111 | | / / _____ / / / _____ / 64*I*\/ 111 | | / / 64*I*\/ 111 128 / / / 64*I*\/ 111 128 3*3 / 64 + ------------ | | / / 64*I*\/ 111 128 / / / 64*I*\/ 111 128 3*3 / 64 + ------------ | | / 2*3 / 64 + ------------ + -------------------------- / / 2*3 / 64 + ------------ + -------------------------- \/ 9 | | / 2*3 / 64 + ------------ + -------------------------- / / 2*3 / 64 + ------------ + -------------------------- \/ 9 | | / \/ 9 ___________________ / / \/ 9 ___________________ | | / \/ 9 ___________________ / / \/ 9 ___________________ | | / / _____ / / / _____ | | / / _____ / / / _____ | | / / 64*I*\/ 111 / / / 64*I*\/ 111 | | / / 64*I*\/ 111 / / / 64*I*\/ 111 | | / 3*3 / 64 + ------------ / / 3*3 / 64 + ------------ | | / 3*3 / 64 + ------------ / / 3*3 / 64 + ------------ | | \/ \/ 9 \/ \/ \/ 9 | | \/ \/ 9 \/ \/ \/ 9 | |-3 + ------------------------------------------------------------------- - --------------------------------------------------------------------------------------------------------------------------------------------------|*|-3 + ------------------------------------------------------------------- + --------------------------------------------------------------------------------------------------------------------------------------------------| \ 2 2 / \ 2 2 /
$$\left(-3 - \frac{i \sqrt{\frac{128}{3 \sqrt[3]{64 + \frac{64 \sqrt{111} i}{9}}} - \frac{64}{\sqrt{\frac{128}{3 \sqrt[3]{64 + \frac{64 \sqrt{111} i}{9}}} + 2 \sqrt[3]{64 + \frac{64 \sqrt{111} i}{9}}}} + 2 \sqrt[3]{64 + \frac{64 \sqrt{111} i}{9}}}}{2} + \frac{\sqrt{\frac{128}{3 \sqrt[3]{64 + \frac{64 \sqrt{111} i}{9}}} + 2 \sqrt[3]{64 + \frac{64 \sqrt{111} i}{9}}}}{2}\right) \left(-3 + \frac{\sqrt{\frac{128}{3 \sqrt[3]{64 + \frac{64 \sqrt{111} i}{9}}} + 2 \sqrt[3]{64 + \frac{64 \sqrt{111} i}{9}}}}{2} + \frac{i \sqrt{\frac{128}{3 \sqrt[3]{64 + \frac{64 \sqrt{111} i}{9}}} - \frac{64}{\sqrt{\frac{128}{3 \sqrt[3]{64 + \frac{64 \sqrt{111} i}{9}}} + 2 \sqrt[3]{64 + \frac{64 \sqrt{111} i}{9}}}} + 2 \sqrt[3]{64 + \frac{64 \sqrt{111} i}{9}}}}{2}\right)$$
=
__________________ ___________________________________________
3 / _____ / _______________ 3 ___ 2/3 ___ 3 ___
4*\/ 27 + 3*I*\/ 111 2/3 / 3 / _____ 8*\/ 3 16*3 4*\/ 2 *\/ 3
9 + ----------------------- - 2*3 * / 2*\/ 9 + I*\/ 111 + ------------------ + -------------------- - ------------------------------------------------
3 / _______________ _______________ _________________________________________
/ 3 / _____ 3 / _____ / _______________ 3 ___
\/ \/ 9 + I*\/ 111 3*\/ 9 + I*\/ 111 / 3 / _____ 4*\/ 3
/ \/ 9 + I*\/ 111 + ------------------
/ _______________
/ 3 / _____
\/ \/ 9 + I*\/ 111
$$9 + \frac{16 \cdot 3^{\frac{2}{3}}}{3 \sqrt[3]{9 + \sqrt{111} i}} - \frac{4 \sqrt{2} \sqrt[3]{3}}{\sqrt{\frac{4 \sqrt[3]{3}}{\sqrt[3]{9 + \sqrt{111} i}} + \sqrt[3]{9 + \sqrt{111} i}}} - 2 \cdot 3^{\frac{2}{3}} \sqrt{\frac{8 \sqrt[3]{3}}{\sqrt[3]{9 + \sqrt{111} i}} + 2 \sqrt[3]{9 + \sqrt{111} i}} + \frac{4 \sqrt[3]{27 + 3 \sqrt{111} i}}{3}$$
9 + 4*(27 + 3*i*sqrt(111))^(1/3)/3 - 2*3^(2/3)*sqrt(2*(9 + i*sqrt(111))^(1/3) + 8*3^(1/3)/(9 + i*sqrt(111))^(1/3)) + 16*3^(2/3)/(3*(9 + i*sqrt(111))^(1/3)) - 4*sqrt(2)*3^(1/3)/sqrt((9 + i*sqrt(111))^(1/3) + 4*3^(1/3)/(9 + i*sqrt(111))^(1/3))
Respuesta numérica
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x1 = -5.1044332934914 + 2.86882170632624*i
x2 = -5.1044332934914 - 2.86882170632624*i
x3 = -0.895566706508598 + 0.791922338882763*i
x4 = -0.895566706508598 - 0.791922338882763*i
x4 = -0.895566706508598 - 0.791922338882763*i