Question

Use your answer in part (a) to find the two values of m for which (m-2)2 -4(m-2)+2=0​

Answer 1

Explanation:

Replace m - 2 with x. Then we have x^2 - 4x + 2 = 0.

Completing the square, we get x^2 - 4x + 4 - 4 + 2 = 0, or

x^2 - 4x + 4 - 2 = 0, or

(x - 2)^2 - 2 = 0, or (x - 2)^2 = 2

Solve for x: Take the square root of both sides. Then:

x - 2 = ±√2 and x = 2 + √2 and x = 2 - √2

But x = m - 2; therefore, x = m - 2 = 2 - √2. Solving for m, we get

m = 4 - √2.

Also: m - 2 = 2 + √2 leads to m = 4 + √2.

The given equation is true for these two values of m.