Let's first simplify the expression by multiplying out (x²-5x+7)²:
(x²-5x+7)² = (x²-5x+7)(x²-5x+7= x⁴ - 5x³ + 7x² - 5x³ + 25x² - 35x + 7x² - 35x + 4= x⁴ - 10x³ + 39x² - 70x + 49
Now we can substitute this back into the original equation:
(x⁴ - 10x³ + 39x² - 70x + 49) - (x²-5x+7) = x⁴ - 10x³ + 39x² - 70x + 49 - x² + 5x - 7 = x⁴ - 10x³ + 38x² - 65x + 42 = 0
This is a fourth-degree polynomial equation. It can be difficult to solve without using numerical methods or graphing software.
Let's first simplify the expression by multiplying out (x²-5x+7)²:
(x²-5x+7)² = (x²-5x+7)(x²-5x+7
= x⁴ - 5x³ + 7x² - 5x³ + 25x² - 35x + 7x² - 35x + 4
= x⁴ - 10x³ + 39x² - 70x + 49
Now we can substitute this back into the original equation:
(x⁴ - 10x³ + 39x² - 70x + 49) - (x²-5x+7) =
x⁴ - 10x³ + 39x² - 70x + 49 - x² + 5x - 7 =
x⁴ - 10x³ + 38x² - 65x + 42 = 0
This is a fourth-degree polynomial equation. It can be difficult to solve without using numerical methods or graphing software.