Given, x^4+64xy^3=0 ⇒ x(x^3+64y^3)=0 ⇒ x(x^3+(4y)^3)=0 ⇒ x(x+4y)(x^2 4xy+16y^2)=0 ⇒ x=0, x= 4y, x^2 4xy+16y^2=0 ⇒ x=4y±√(16y^2 64y ...

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Factorisation Using Algebraic Identities

Solve:- x4 +...

Question

Solve:-
$x^{4} + 64 x y^{3}$

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Solution

Given, $x^{4} + 64 x y^{3} = 0$

$\Rightarrow x (x^{3} + 64 y^{3}) = 0$

$\Rightarrow x (x^{3} + (4 y)^{3}) = 0$

$\Rightarrow x (x + 4 y) (x^{2} - 4 x y + 16 y^{2}) = 0$

$\Rightarrow x = 0, x = - 4 y, x^{2} - 4 x y + 16 y^{2} = 0$

$\Rightarrow x = \frac{4 y \pm \sqrt{16 y^{2} - 64 y^{2}}}{2}$

$= \frac{4 y \pm \sqrt{- 48 y^{2}}}{2}$

$= \frac{4 y \pm i y \sqrt{- 48}}{2}$

$= \frac{4 y \pm i y 4 \sqrt{3}}{2}$

$= 2 y \pm i 2 \sqrt{3} y$

$∴ x = 0, x = - 4 y, x = 2 y \pm i 2 \sqrt{3} y$

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