Question

What are the solutions of the equation (x-3)2 + 2(x – 3) - 8= 0? Use u substitution to solve.

x=-5 and x=1
x=-1 and x=5
x=-1 and x=-7
x=1 andx=7

Answer 1

x = - 1 and x = 5

Explanation:

Given

(x - 3)² + 2(x - 3) - 8 = 0

Let u = x - 3, then

u² + 2u - 8 = 0 ← solve for u

(u + 4)(u - 2) = 0 ← in factored form

Equate each factor to zero and solve for u

u + 4 = 0 ⇒ u = - 4

u - 2 = 0 ⇒ u = 2

Convert back to x, that is

x - 3 = - 4 ( add 3 to both sides ) ⇒ x = - 1

x - 3 = 2 ( add 3 to both sides ) ⇒ x = 5

Answer 2

Answer: The correct option is

(B) x = -1 and x = 5.

Step-by-step explanation: We are given the following equation :

`(x-3)^2+2(x-3)-8=0~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)`

We are to find the solutions of the above equation.

Let u= (x-3).

Then, from equation (i), we have

`u^2+2u-8=0\\\\\Rightarrow u^2+4u-2u-8=0\\\\\Rightarrow u(u+4)-2(u+4)=0\\\\\Rightarrow (u-2)(u+4)=0\\\\\Rightarrow u-2=0,~~~~~~~~~~~~u+4=0\\\\\Rightarrow x-3-2=0,~~~\Rightarrow x-3+4=0\\\\\Rightarrow x=5,~x=-1.`

Thus, the required solution is x = -1 and x = 5.

Option (B) is CORRECT.