Question

How to answer this pls.

Give the solution and checking plz.
Help. this is Equation with Radicals. ​

Answer 1

x = 11.61 to the nearest hundredth.

Explanation:

√(2x - 2) = x - 7

Square both sides:

2x - 2 = (x - 7)^2

2x - 2 = x^2 - 14x + 49

x^2 - 16x + 51 = 0

using the quadratic formula we get x = 4.39 , 11.61.

With radical equations we can get extraneous roots so we check these values:

X = 4.39 :

√(2(4.39) - 2) = 2.61

4.39 - 7 = -2.61 so 4.39 is NOT a root.

x = 11.61

√(2(11.61) - 2) = 4.61

11.61 - 7 = 4.61 so this is a root.