Question

(x-5)^2-(3x+2)^2=(4x-1)(x-4)

Answer 1

Решено!!!)))))))))))))

Answer 2

Let's solve the given equation step-by-step:

1. Expand the squares on the left-hand side (LHS): (x-5)^2 - (3x+2)^2 = (x-5)(x-5) - (3x+2)(3x+2) = x^2 - 10x + 25 - (9x^2 + 12x + 4) = x^2 - 10x + 25 - 9x^2 - 12x - 4 = -8x^2 - 22x + 21

2. Expand the right-hand side (RHS): (4x-1)(x-4) = 4x^2 - 16x - x + 4 = 4x^2 - 17x + 4

Now, we have the equation: -8x^2 - 22x + 21 = 4x^2 - 17x + 4

3. Move all terms to one side to set the equation to zero: -8x^2 - 22x + 21 - (4x^2 - 17x + 4) = 0 -8x^2 - 22x + 21 - 4x^2 + 17x - 4 = 0 -12x^2 - 5x + 17 = 0

At this point, we have a quadratic equation: -12x^2 - 5x + 17 = 0

4. Solve the quadratic equation using any method you prefer, such as factoring, completing the square, or using the quadratic formula.

Alternatively, we can use the quadratic formula to find the solutions:

The quadratic formula is given by: x = (-b ± √(b^2 - 4ac)) / 2a

For the equation -12x^2 - 5x + 17 = 0, we have: a = -12, b = -5, c = 17

x = (5 ± √((-5)^2 - 4 * (-12) * 17)) / 2 * (-12) x = (5 ± √(25 + 816)) / -24 x = (5 ± √841) / -24 x = (5 ± 29) / -24

So the two possible solutions are:

1. x = (5 + 29) / -24 = 34 / -24 = -17/12
2. x = (5 - 29) / -24 = -24 / -24 = 1

Therefore, the equation has two solutions: x = -17/12 and x = 1.