(√3–√2+x)(√3–√2+x)=x

Answer 1

Let's expand the left-hand side of the equation:

(√3 – √2 + x)(√3 – √2 + x) = (√3 – √2)(√3 – √2) + (√3 – √2)x + (√3 – √2)x + x^2
= (3 – 2√6 + 2) + 2x(√3 – √2) + x^2
= 4 + 2x(√3 – √2) + x^2

Since we want this expression to equal x, we have the equation:

4 + 2x(√3 – √2) + x^2 = x

Rearranging the terms to make it a quadratic equation, we have:

x^2 + (2√3 – 1)x + (4 – 2√6) = 0

This is a quadratic equation in x. To solve for x, we can use the quadratic formula:

x = [-b ± √(b^2 - 4ac)] / (2a)

In this case, a = 1, b = 2√3 – 1, and c = 4 – 2√6. Substituting these values into the quadratic formula, we can solve for x.