Question

Identify all of the following solutions of square root of x minus 8 end root plus 8 equals x.

x = 8
x = 9
x = 8 and x = 9
None of the above

Answer 1

Explanation:

According to the question, the equation becomes,

`√(x-8)+8=x`

⇒
`√(x-8)=x-8`

Squaring on both the sides, we get

⇒
`x-8=(x-8)^2`

⇒
`x-8=x^2-16x+64`

⇒
`x^2-16x-x+64+8=0`

⇒
`x^2-17x+72=0`

⇒
`x^2-8x-9x+72=0`

⇒
`x(x-8)-9(x-8)=0`

⇒
`(x-8)(x-9)=0`

Then, (x-8)=0

⇒x=8

and (x-9)=0

⇒x=9

Thus, the solution of the given equation is x=8 and x=9.

Answer 2

`√(x-8) +8=x \\ √(x-8) =x-8 \\ {( √(x-8) )}^(2) = {(x-8)}^(2) \\ x-8= x^(2) -16x+64 \\ x^(2) -16x-x+64+8=0 \\ x^(2) -17x+72=0`


`(x-8)(x-9)=0 \\ x-8=0 \ and \ x-9=0 \\ x=8 \ and \ x=9`