Question

Show all work to solve the equation for x. If a solution is extraneous, be sure to identify it. Square root of the quantity x + 6 end quantity - 4 = x.

Answer 1

x = 2 is the solution of the given equation

Explanation:

Step(i):-

Given equation

`√(x+6-4) = x`

squaring on both sides , we get

`(√(x+2))^(2) = x^(2)`

⇒ x + 2 = x²

⇒x² - x -2 =0

Step(ii):-

Given x² - x -2 =0

⇒ x² - 2x + x - 2 =0

⇒ x ( x-2) + 1(x - 2) =0

⇒ (x + 1) ( x-2) =0

⇒ x = -1 and x =2

x = 2 is the solution of the given equation

Verification:-

`√(x+6-4) = x`

Put x= 2

`√(2+6-4) = 2`

`√(4) = 2`

2 = 2