Sr Examen
Otras calculadoras
-
¿Cómo usar?
- La ecuación:
-
Ecuación x^2+5x=36
-
Ecuación 9-7(x+3)=5-6x
-
Ecuación 4x-5=3+2(x+1)
-
Ecuación 6/(x-2)+5/x=3
- Expresar {x} en función de y en la ecuación:
- -14*x-12*y=-13
- -20*x+14*y=16
- -7*x+15*y=-11
- -14*x+5*y=3
-
Expresiones idénticas
- (x+ cinco)*(x- dos)+ tres *sqrt(x+ tres)= cero
- (x más 5) multiplicar por (x menos 2) más 3 multiplicar por raíz cuadrada de (x más 3) es igual a 0
- (x más cinco) multiplicar por (x menos dos) más tres multiplicar por raíz cuadrada de (x más tres) es igual a cero
- (x+5)*(x-2)+3*√(x+3)=0
- (x+5)(x-2)+3sqrt(x+3)=0
- x+5x-2+3sqrtx+3=0
- (x+5)*(x-2)+3*sqrt(x+3)=O
-
Expresiones semejantes
- (x+5)*(x+2)+3*sqrt(x+3)=0
- (x-5)*(x-2)+3*sqrt(x+3)=0
- (x+5)*(x-2)-3*sqrt(x+3)=0
- (x+5)*(x-2)+3*sqrt(x-3)=0
-
Expresiones con funciones
- Raíz cuadrada sqrt
- sqrt((a-b*w^2)^2+(c*w)^2)=(19/10)*w
- sqrt(0*x+0)=0
- sqrt(5+2*x)=8+-sqrt(x-1)
- sqrt(4*x^2+4*x-6)=2
- sqrt(3*x+1)=x-1
(x+5)*(x-2)+3*sqrt(x+3)=0 la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Ha introducido
[src]
_______ (x + 5)*(x - 2) + 3*\/ x + 3 = 0
$$\left(x - 2\right) \left(x + 5\right) + 3 \sqrt{x + 3} = 0$$
Respuesta rápida
[src]
x1 = 1
$$x_{1} = 1$$
_________________ / _________________ \
/ ______ | / ______ |
/ 1033 \/ 1965 | ___ / 1033 \/ 1965 |
3 / ---- + -------- | \/ 3 *3 / ---- + -------- ___ |
7 61 \/ 54 6 | \/ 54 6 61*\/ 3 |
x2 = - - - ------------------------- - ---------------------- + I*|- ---------------------------- + -------------------------|
3 _________________ 2 | 2 _________________|
/ ______ | / ______ |
/ 1033 \/ 1965 | / 1033 \/ 1965 |
18*3 / ---- + -------- | 18*3 / ---- + -------- |
\/ 54 6 \ \/ 54 6 /
$$x_{2} = - \frac{7}{3} - \frac{\sqrt[3]{\frac{\sqrt{1965}}{6} + \frac{1033}{54}}}{2} - \frac{61}{18 \sqrt[3]{\frac{\sqrt{1965}}{6} + \frac{1033}{54}}} + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{1965}}{6} + \frac{1033}{54}}}{2} + \frac{61 \sqrt{3}}{18 \sqrt[3]{\frac{\sqrt{1965}}{6} + \frac{1033}{54}}}\right)$$
_________________ / _________________ \
/ ______ | / ______ |
/ 1033 \/ 1965 | ___ / 1033 \/ 1965 |
3 / ---- + -------- |\/ 3 *3 / ---- + -------- ___ |
7 61 \/ 54 6 | \/ 54 6 61*\/ 3 |
x3 = - - - ------------------------- - ---------------------- + I*|---------------------------- - -------------------------|
3 _________________ 2 | 2 _________________|
/ ______ | / ______ |
/ 1033 \/ 1965 | / 1033 \/ 1965 |
18*3 / ---- + -------- | 18*3 / ---- + -------- |
\/ 54 6 \ \/ 54 6 /
$$x_{3} = - \frac{7}{3} - \frac{\sqrt[3]{\frac{\sqrt{1965}}{6} + \frac{1033}{54}}}{2} - \frac{61}{18 \sqrt[3]{\frac{\sqrt{1965}}{6} + \frac{1033}{54}}} + i \left(- \frac{61 \sqrt{3}}{18 \sqrt[3]{\frac{\sqrt{1965}}{6} + \frac{1033}{54}}} + \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{1965}}{6} + \frac{1033}{54}}}{2}\right)$$
x3 = -7/3 - (sqrt(1965)/6 + 1033/54)^(1/3)/2 - 61/(18*(sqrt(1965)/6 + 1033/54)^(1/3)) + i*(-61*sqrt(3)/(18*(sqrt(1965)/6 + 1033/54)^(1/3)) + sqrt(3)*(sqrt(1965)/6 + 1033/54)^(1/3)/2)
Suma y producto de raíces
[src]
suma
_________________ / _________________ \ _________________ / _________________ \
/ ______ | / ______ | / ______ | / ______ |
/ 1033 \/ 1965 | ___ / 1033 \/ 1965 | / 1033 \/ 1965 | ___ / 1033 \/ 1965 |
3 / ---- + -------- | \/ 3 *3 / ---- + -------- ___ | 3 / ---- + -------- |\/ 3 *3 / ---- + -------- ___ |
7 61 \/ 54 6 | \/ 54 6 61*\/ 3 | 7 61 \/ 54 6 | \/ 54 6 61*\/ 3 |
1 + - - - ------------------------- - ---------------------- + I*|- ---------------------------- + -------------------------| + - - - ------------------------- - ---------------------- + I*|---------------------------- - -------------------------|
3 _________________ 2 | 2 _________________| 3 _________________ 2 | 2 _________________|
/ ______ | / ______ | / ______ | / ______ |
/ 1033 \/ 1965 | / 1033 \/ 1965 | / 1033 \/ 1965 | / 1033 \/ 1965 |
18*3 / ---- + -------- | 18*3 / ---- + -------- | 18*3 / ---- + -------- | 18*3 / ---- + -------- |
\/ 54 6 \ \/ 54 6 / \/ 54 6 \ \/ 54 6 /
$$\left(1 + \left(- \frac{7}{3} - \frac{\sqrt[3]{\frac{\sqrt{1965}}{6} + \frac{1033}{54}}}{2} - \frac{61}{18 \sqrt[3]{\frac{\sqrt{1965}}{6} + \frac{1033}{54}}} + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{1965}}{6} + \frac{1033}{54}}}{2} + \frac{61 \sqrt{3}}{18 \sqrt[3]{\frac{\sqrt{1965}}{6} + \frac{1033}{54}}}\right)\right)\right) + \left(- \frac{7}{3} - \frac{\sqrt[3]{\frac{\sqrt{1965}}{6} + \frac{1033}{54}}}{2} - \frac{61}{18 \sqrt[3]{\frac{\sqrt{1965}}{6} + \frac{1033}{54}}} + i \left(- \frac{61 \sqrt{3}}{18 \sqrt[3]{\frac{\sqrt{1965}}{6} + \frac{1033}{54}}} + \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{1965}}{6} + \frac{1033}{54}}}{2}\right)\right)$$
=
/ _________________ \ / _________________ \
| / ______ | | / ______ |
_________________ | ___ / 1033 \/ 1965 | | ___ / 1033 \/ 1965 |
/ ______ |\/ 3 *3 / ---- + -------- ___ | | \/ 3 *3 / ---- + -------- ___ |
11 / 1033 \/ 1965 61 | \/ 54 6 61*\/ 3 | | \/ 54 6 61*\/ 3 |
- -- - 3 / ---- + -------- - ------------------------ + I*|---------------------------- - -------------------------| + I*|- ---------------------------- + -------------------------|
3 \/ 54 6 _________________ | 2 _________________| | 2 _________________|
/ ______ | / ______ | | / ______ |
/ 1033 \/ 1965 | / 1033 \/ 1965 | | / 1033 \/ 1965 |
9*3 / ---- + -------- | 18*3 / ---- + -------- | | 18*3 / ---- + -------- |
\/ 54 6 \ \/ 54 6 / \ \/ 54 6 /
$$- \frac{11}{3} - \sqrt[3]{\frac{\sqrt{1965}}{6} + \frac{1033}{54}} - \frac{61}{9 \sqrt[3]{\frac{\sqrt{1965}}{6} + \frac{1033}{54}}} + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{1965}}{6} + \frac{1033}{54}}}{2} + \frac{61 \sqrt{3}}{18 \sqrt[3]{\frac{\sqrt{1965}}{6} + \frac{1033}{54}}}\right) + i \left(- \frac{61 \sqrt{3}}{18 \sqrt[3]{\frac{\sqrt{1965}}{6} + \frac{1033}{54}}} + \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{1965}}{6} + \frac{1033}{54}}}{2}\right)$$
producto
/ _________________ / _________________ \\ / _________________ / _________________ \\ | / ______ | / ______ || | / ______ | / ______ || | / 1033 \/ 1965 | ___ / 1033 \/ 1965 || | / 1033 \/ 1965 | ___ / 1033 \/ 1965 || | 3 / ---- + -------- | \/ 3 *3 / ---- + -------- ___ || | 3 / ---- + -------- |\/ 3 *3 / ---- + -------- ___ || | 7 61 \/ 54 6 | \/ 54 6 61*\/ 3 || | 7 61 \/ 54 6 | \/ 54 6 61*\/ 3 || |- - - ------------------------- - ---------------------- + I*|- ---------------------------- + -------------------------||*|- - - ------------------------- - ---------------------- + I*|---------------------------- - -------------------------|| | 3 _________________ 2 | 2 _________________|| | 3 _________________ 2 | 2 _________________|| | / ______ | / ______ || | / ______ | / ______ || | / 1033 \/ 1965 | / 1033 \/ 1965 || | / 1033 \/ 1965 | / 1033 \/ 1965 || | 18*3 / ---- + -------- | 18*3 / ---- + -------- || | 18*3 / ---- + -------- | 18*3 / ---- + -------- || \ \/ 54 6 \ \/ 54 6 // \ \/ 54 6 \ \/ 54 6 //
$$\left(- \frac{7}{3} - \frac{\sqrt[3]{\frac{\sqrt{1965}}{6} + \frac{1033}{54}}}{2} - \frac{61}{18 \sqrt[3]{\frac{\sqrt{1965}}{6} + \frac{1033}{54}}} + i \left(- \frac{61 \sqrt{3}}{18 \sqrt[3]{\frac{\sqrt{1965}}{6} + \frac{1033}{54}}} + \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{1965}}{6} + \frac{1033}{54}}}{2}\right)\right) \left(- \frac{7}{3} - \frac{\sqrt[3]{\frac{\sqrt{1965}}{6} + \frac{1033}{54}}}{2} - \frac{61}{18 \sqrt[3]{\frac{\sqrt{1965}}{6} + \frac{1033}{54}}} + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{1965}}{6} + \frac{1033}{54}}}{2} + \frac{61 \sqrt{3}}{18 \sqrt[3]{\frac{\sqrt{1965}}{6} + \frac{1033}{54}}}\right)\right)$$
=
2/3 ____________________ ____________________
/ ______\ 3 / ______ 2/3 ______ 3 / ______ 2/3 ______
4*\1033 + 9*\/ 1965 / 629*\/ 2066 + 18*\/ 1965 4891*2 \/ 1965 *\/ 2066 + 18*\/ 1965 7*2 *\/ 1965
- ------------------------ + --------------------------- + --------- + -------------------------------- + ---------------
3 6 6 2 2
-------------------------------------------------------------------------------------------------------------------------
2/3
/ ______\
\1033 + 9*\/ 1965 /
$$\frac{- \frac{4 \left(9 \sqrt{1965} + 1033\right)^{\frac{2}{3}}}{3} + \frac{7 \sqrt{1965} \cdot 2^{\frac{2}{3}}}{2} + \frac{\sqrt{1965} \sqrt[3]{18 \sqrt{1965} + 2066}}{2} + \frac{4891 \cdot 2^{\frac{2}{3}}}{6} + \frac{629 \sqrt[3]{18 \sqrt{1965} + 2066}}{6}}{\left(9 \sqrt{1965} + 1033\right)^{\frac{2}{3}}}$$
(-4*(1033 + 9*sqrt(1965))^(2/3)/3 + 629*(2066 + 18*sqrt(1965))^(1/3)/6 + 4891*2^(2/3)/6 + sqrt(1965)*(2066 + 18*sqrt(1965))^(1/3)/2 + 7*2^(2/3)*sqrt(1965)/2)/(1033 + 9*sqrt(1965))^(2/3)
Respuesta numérica
[src]
x1 = 1.0
x2 = -4.96078509762886 - 0.614145738213459*i
x3 = -4.96078509762886 + 0.614145738213459*i
x3 = -4.96078509762886 + 0.614145738213459*i