Question

Please help me with this question. I tried making 1 equal to 0^(x^2-5x+2) already but my teacher says that I have to use another way.

Answer 1

9

Explanation:

If you have mⁿ = 1, then either m = 1 or n = 0.

Setting the base equal to 1:

x² − 4x + 2 = 1

x² − 4x + 1 = 0

For a quadratic equation ax² + bx + c = 0, the sum of the roots is equal to -b/a.

-(-4) / 1 = 4

Setting the exponent equal to 0:

x² − 5x + 2 = 0

Sum of the roots:

-(-5) / 1 = 5

The sum of all real numbers of x that satisfy the equation is 4 + 5 = 9.