Question

# 50 points ✨

⏬⏬⏬⏬

♦ (X+2)³= x(x²-1) ♦

❌DON'T SPAM❌

☑ Need Quality ANSWER☺

Answer 1

Answer:

Given :

( x + 2 )³ = x ( x² - 1  )

⇒ ( x + 2 )³ = x³ - x

We know that ( a + b )³ = a³ + b³ + 3 ab ( a + b )

⇒ x³ + 2³ + 3 × 2 × x ( x + 2 ) = x³ - x

⇒ x³ + 8 + 6 x ( x + 2 ) = x³ - x

Cancel the x³ from both sides :

⇒ 8 + 6 x ( x + 2 ) = - x

⇒ 8 + 6 x² + 12 x + x = 0

⇒ 6 x² + 13 x + 8 = 0

The above equation when compared with ,

a x² + b x + c = 0 gives :

a =  6

b = 13

c = 8

$x=\dfrac{-b\pm \sqrt{b^2-4ac}}{2a}\\\\\implies x=\dfrac{-13\pm \sqrt{169-4\times 48}}{2\times 6}\\\\\implies x=\dfrac{-13\pm \sqrt{169-192}}{12}\\\\\implies x=\dfrac{-13\pm\sqrt{-33}}{12}\\\\\implies \boxed{x=\dfrac{-13\pm \sqrt{33}i}{12}}$

Step-by-step explanation:

First of all open all the brackets . Cubing the LHS will require us to use the identity of ( a + b )³ .

After that we can reduce the equation to a quadratic equation .

The solutions of quadratic equation can be easily found by the quadratic formula .

Here the square root of a negative number is an imaginary number and is denoted by i .

Note that roots are complex and not real !

Answer 2

Here is your answer ☺️☺️❤️❤️

.

.

.

.

Hope this helps you ❤️❤️☺️☺️