Sr Examen

Otras calculadoras

Descomponer -y^4-y^2-5 al cuadrado

Expresión a simplificar:

Solución

Ha introducido [src]
   4    2    
- y  - y  - 5
(y4y2)5\left(- y^{4} - y^{2}\right) - 5
-y^4 - y^2 - 5
Simplificación general [src]
      2    4
-5 - y  - y 
y4y25- y^{4} - y^{2} - 5
-5 - y^2 - y^4
Factorización [src]
/             /    /  ____\\              /    /  ____\\\ /             /    /  ____\\              /    /  ____\\\ /               /    /  ____\\              /    /  ____\\\ /               /    /  ____\\              /    /  ____\\\
|    4 ___    |atan\\/ 19 /|     4 ___    |atan\\/ 19 /|| |    4 ___    |atan\\/ 19 /|     4 ___    |atan\\/ 19 /|| |      4 ___    |atan\\/ 19 /|     4 ___    |atan\\/ 19 /|| |      4 ___    |atan\\/ 19 /|     4 ___    |atan\\/ 19 /||
|x + \/ 5 *sin|------------| + I*\/ 5 *cos|------------||*|x + \/ 5 *sin|------------| - I*\/ 5 *cos|------------||*|x + - \/ 5 *sin|------------| + I*\/ 5 *cos|------------||*|x + - \/ 5 *sin|------------| - I*\/ 5 *cos|------------||
\             \     2      /              \     2      // \             \     2      /              \     2      // \               \     2      /              \     2      // \               \     2      /              \     2      //
(x+(54sin(atan(19)2)54icos(atan(19)2)))(x+(54sin(atan(19)2)+54icos(atan(19)2)))(x+(54sin(atan(19)2)+54icos(atan(19)2)))(x+(54sin(atan(19)2)54icos(atan(19)2)))\left(x + \left(\sqrt[4]{5} \sin{\left(\frac{\operatorname{atan}{\left(\sqrt{19} \right)}}{2} \right)} - \sqrt[4]{5} i \cos{\left(\frac{\operatorname{atan}{\left(\sqrt{19} \right)}}{2} \right)}\right)\right) \left(x + \left(\sqrt[4]{5} \sin{\left(\frac{\operatorname{atan}{\left(\sqrt{19} \right)}}{2} \right)} + \sqrt[4]{5} i \cos{\left(\frac{\operatorname{atan}{\left(\sqrt{19} \right)}}{2} \right)}\right)\right) \left(x + \left(- \sqrt[4]{5} \sin{\left(\frac{\operatorname{atan}{\left(\sqrt{19} \right)}}{2} \right)} + \sqrt[4]{5} i \cos{\left(\frac{\operatorname{atan}{\left(\sqrt{19} \right)}}{2} \right)}\right)\right) \left(x + \left(- \sqrt[4]{5} \sin{\left(\frac{\operatorname{atan}{\left(\sqrt{19} \right)}}{2} \right)} - \sqrt[4]{5} i \cos{\left(\frac{\operatorname{atan}{\left(\sqrt{19} \right)}}{2} \right)}\right)\right)
(((x + 5^(1/4)*sin(atan(sqrt(19))/2) + i*5^(1/4)*cos(atan(sqrt(19))/2))*(x + 5^(1/4)*sin(atan(sqrt(19))/2) - i*5^(1/4)*cos(atan(sqrt(19))/2)))*(x - 5^(1/4)*sin(atan(sqrt(19))/2) + i*5^(1/4)*cos(atan(sqrt(19))/2)))*(x - 5^(1/4)*sin(atan(sqrt(19))/2) - i*5^(1/4)*cos(atan(sqrt(19))/2))
Expresión del cuadrado perfecto
Expresemos el cuadrado perfecto del trinomio cuadrático
(y4y2)5\left(- y^{4} - y^{2}\right) - 5
Para eso usemos la fórmula
ay4+by2+c=a(m+y2)2+na y^{4} + b y^{2} + c = a \left(m + y^{2}\right)^{2} + n
donde
m=b2am = \frac{b}{2 a}
n=4acb24an = \frac{4 a c - b^{2}}{4 a}
En nuestro caso
a=1a = -1
b=1b = -1
c=5c = -5
Entonces
m=12m = \frac{1}{2}
n=194n = - \frac{19}{4}
Pues,
(y2+12)2194- \left(y^{2} + \frac{1}{2}\right)^{2} - \frac{19}{4}
Respuesta numérica [src]
-5.0 - y^2 - y^4
-5.0 - y^2 - y^4
Combinatoria [src]
      2    4
-5 - y  - y 
y4y25- y^{4} - y^{2} - 5
-5 - y^2 - y^4
Denominador racional [src]
      2    4
-5 - y  - y 
y4y25- y^{4} - y^{2} - 5
-5 - y^2 - y^4
Unión de expresiones racionales [src]
      2 /      2\
-5 + y *\-1 - y /
y2(y21)5y^{2} \left(- y^{2} - 1\right) - 5
-5 + y^2*(-1 - y^2)
Compilar la expresión [src]
      2    4
-5 - y  - y 
y4y25- y^{4} - y^{2} - 5
-5 - y^2 - y^4
Parte trigonométrica [src]
      2    4
-5 - y  - y 
y4y25- y^{4} - y^{2} - 5
-5 - y^2 - y^4
Denominador común [src]
      2    4
-5 - y  - y 
y4y25- y^{4} - y^{2} - 5
-5 - y^2 - y^4
Potencias [src]
      2    4
-5 - y  - y 
y4y25- y^{4} - y^{2} - 5
-5 - y^2 - y^4