Question

При каких значениях переменной x выражения x^2-2x+1 и 4x^2-3x-3 равны?

Answer 1

Смотрите решение в прикреплённом файле.

Answer 2

Values of x for the Expressions to be Equal

The values of variable x for which the expressions x^2 - 2x + 1 and 4x^2 - 3x - 3 are equal can be found by setting the two expressions equal to each other and solving for x.

Setting the two expressions equal to each other: x^2 - 2x + 1 = 4x^2 - 3x - 3

Solving for x: 3x^2 - x - 4 = 0

The solutions for x can be found using the quadratic formula: x = (-b ± √(b^2 - 4ac)) / (2a)

Where a = 3, b = -1, and c = -4.

Using the quadratic formula, the solutions for x are: x = (-(-1) ± √((-1)^2 - 4*3*(-4))) / (2*3) x = (1 ± √(49)) / 6 x = (1 ± 7) / 6 x = (1 + 7) / 6 or x = (1 - 7) / 6 x = 8 / 6 or x = -6 / 6 x = 4/3 or x = -1

Therefore, the values of x for which the expressions x^2 - 2x + 1 and 4x^2 - 3x - 3 are equal are x = 4/3 and x = -1.