Question

Solve for x, if a solution is extraneous identify in the final answer. thx :)

Answer 1

x = 6 and x = 11.

Explanation:

sqrt(x - 2) + 8 = x

sqrt(x - 2) = x - 8

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

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

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

x^2 - 17x + 66 = 0

We can use the discriminant to find whether there are solutions to the equation.

b^2 - 4ac; where a = 1, b = -17, and c = 66.

(-17)^2 - 4 * 1 * 66

= 289 - 264

= 25

Since the discriminant is positive, we know there are two valid solutions to the equation.

x^2 - 17x + 66 = 0

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

The solutions are when x - 6 = 0 and x - 11 = 0.

x - 6 = 0

x = 6

x - 11 = 0

x = 11

Hope this helps!

Answer 2

x=11 solution

x=6 extraneous

Explanation:

sqrt( x-2) + 8 = x

Subtract x from each side

sqrt(x-2) = x-8

Square each side

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

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

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

Subtract ( x-2) from each side

0 = x^2 -17x +66

Factor

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

Using the zero product property

x=6 x=11

Checking the solutions

x=6

sqrt( 6-2) + 8 = 6

sqrt(4) +8 = 6

2 +8 = 6

False not a solution

x=11

sqrt( 11-2) + 8 = 11

sqrt(9) +8 =11

3 +8 = 11

solution