Question

(a-2x)^2=. (ab-1)^2=.

Answer 1

(а-2х)^2=2а-4х
(ab-1)^2=4ab-2

Answer 2

To solve the given equations, let's expand and simplify them step by step.

1. Equation: (a - 2x)^2 = 0

Expanding the equation using the identity (a - b)^2 = a^2 - 2ab + b^2:

(a - 2x)^2 = a^2 - 2(2x)(a) + (2x)^2 = a^2 - 4ax + 4x^2

Setting the expression equal to zero:

a^2 - 4ax + 4x^2 = 0

This is a quadratic equation in terms of 'a.' To solve it, we can use the quadratic formula:

a = (-b ± √(b^2 - 4ac)) / (2a)

In this case, a = 1, b = -4x, and c = 4x^2. Substituting these values into the quadratic formula:

a = (-(-4x) ± √((-4x)^2 - 4(1)(4x^2))) / (2(1)) = (4x ± √(16x^2 - 16x^2)) / 2 = (4x ± √0) / 2 = (4x ± 0) / 2 = 4x / 2 = 2x

Therefore, the solution to the equation (a - 2x)^2 = 0 is a = 2x.

2. Equation: (ab - 1)^2 = 0

Expanding the equation using the identity (a - b)^2 = a^2 - 2ab + b^2:

(ab - 1)^2 = (ab)^2 - 2(ab)(1) + 1^2 = a^2b^2 - 2ab + 1

Setting the expression equal to zero:

a^2b^2 - 2ab + 1 = 0

This equation does not factorize further, so we can solve it by applying the quadratic formula as before. However, in this case, the variable 'a' and 'b' are multiplied together, which means the solution may involve complex numbers.

Using the quadratic formula:

ab = (-(-2) ± √((-2)^2 - 4(1)(1))) / (2(1)) ab = (2 ± √(4 - 4)) / 2 ab = (2 ± √0) / 2 ab = (2 ± 0) / 2

ab = 2/2 = 1 (real solution)

Therefore, the solution to the equation (ab - 1)^2 = 0 is ab = 1.

Note: Since the equations were set equal to zero, the solutions obtained are values that make the equations true.