Question

( x + 2 )³ = x³ - 4 solve the quadratic equation by the method of perfect of the square​

Answer 1

Answer:

x^3+6x^2+12x+8=x^3-4

6x^2+12x+12=0

x^2+2x+2=0

(x+1)^2+1=0

(x+1)^2=-1

Answer 2

Given,

( x + 2 )³ = x³ - 4

To Find,

Solve the equation by the method of perfect of the square​ =?

Solution,

$( x + 2 )^3 = x^3 - 4$

Solving using the formula, $(a + b)^3 = a^3 + b^3 + 3a^2b + 3ab^2$$x^3 + 2^3 + 3x^22+ 3x2^2= x^3 - 4\\x^3 + 8 + 6 x^2 + 12x -x^3 + 4 = 0\\ 6 x^2 + 12x + 12 = 0\\6( x^2 + 2x + 2) = 0 \\x^2 + 2x + 2 = 0\\(x + 1)^2 + 1 =0\\(x + 1)^2 = -1$

Hence, $(x + 1)^2 = -1$ is the solution of the equation ( x + 2 )³ = x³ - 4 .