solve the equation.

Question

(2x-1)^2(x-5)^2+(2x-1)^3(x-5)=.0

I have been trying for awhile no success.?

Answer 1

The equation is (2x - 1)² (x - 5)² + (2x - 1)³ (x - 5) = 0.

Common out the term (2x - 1)² (x - 5).

(2x - 1)²(x - 5)[x - 5 + 2x - 1] = 0

(2x - 1)²(x - 5)(3x - 6) = 0

Apply zero product property.

(2x - 1)² = 0, x - 5 = 0 and 3x - 6 = 0

2x - 1 = 0, x = 5 and 3x = 6

2x = 1, x = 5 and x = 2

x = 1/2,1/2, x = 5, and x = 2.

Therefore, the solutions are x = 1/2, 1/2, x = 5, and x = 2.