Question

Please help me with this! :

Answer 1

Answer:

x=11

6 is extraneous

Step-by-step explanation:

sqrt( x-2) +8=x

Subtract 8 from each side

sqrt( x-2) +8-8=x-8

sqrt(x-2) = x-8

Square each side

(sqrt(x-2))^2 = (x-8)^2

x-2 = (x-8) (x-8)

x-2 = x^2 - 8x -8x +64

x-2 = x^2 - 16x +64

Subtract x from each side

x-x-2 = x^2 - 16x -x +64

-2 = x^2 - 17x +64

Add 2 to each side

-2+2 =x^2 - 17x  +64+2

0 = x^2 - 17x  +66

Factor

0 = (x- 11) (x-6)

Using the zero product property

x-11=0   x-6 =0

x=11       x=6

Check the solutions

x=11

sqrt( 11-2) +8=11

sqrt(9) +8 =11

3+8 =11  true

x=6

sqrt( 6-2) +8=6

sqrt(4) +8 =6

2 +8 = 6  false