Question 1

Explanation

Given the function $f(x) = 2x - 1$. We want to find the value of $x_1 + x_2$ that satisfies the equation $6f(x^2) - f^2(x) = 6x^2 - x$.

First, we find the forms of $f(x^2)$ and $f^2(x)$ or $(f(x))^2$.

Next, we substitute these results into the given equation.

We move all terms to the left side to form a quadratic equation $ax^2 + bx + c = 0$.

From the quadratic equation $2x^2 + 5x - 7 = 0$, we get $a = 2$, $b = 5$, and $c = -7$.

The sum of the roots of the quadratic equation ($x_1 + x_2$) can be calculated using the formula $-\frac{b}{a}$.

So, the value of $x_1 + x_2$ is $-\frac{5}{2}$.