If the expression f^2 +g^4 -2f+1 is rewritten in the form a^2 +(g^2)^2 What most be the value of a

Question

If the expression f^2 +g^4 -2f+1 is rewritten in the form a^2 +(g^2)^2 What most be the value of a

Answer 1

By regrouping terms we write

f² + g⁴ - 2f + 1 = (f² - 2f + 1) + g⁴ = (f - 1)² + (g²)²

Thus a² = (f - 1)². There are two solutions, a = ± (f - 1).