Question

(2x^2-2x)^2+2(x^2-2x)-15=0

Answer 1

( (x - 5)(x + 5))^2 + ((x - 3)(x + 5))^2 = 0(x + 5)( (x -5)^2 + (x - 3)^2) = 0( x + 5)( x^2-10x +25+ x^2-6x+ 9) = 0( x + 5)( 2x^2 -16x + 34) = 0x + 5 = 0x = - 52x^2 - 16x + 34 = 0x^2 - 8x + 17 = 0D = b^2 - 4ac = 64 - 68 = - 4 дискриминант отрицательный,значит,корней нет.Ответ: x = - 5

Answer 2

To solve the quadratic equation $(2x^2 - 2x)^2 + 2(x^2 - 2x) - 15 = 0$, you can start by simplifying the equation and then factorizing it. Let's break it down step by step:

1. Expand the equation:

   $(2x^2 - 2x)^2 + 2(x^2 - 2x) - 15 = 0$

   Expand $(2x^2 - 2x)^2$:

   $(4x^4 - 8x^3 + 4x^2) + (2x^2 - 4x) - 15 = 0$

2. Combine like terms:

   $4x^4 - 8x^3 + 6x^2 - 4x - 15 = 0$

3. Now, try to factorize the quadratic equation if possible.

   Unfortunately, this equation cannot be easily factorized into linear factors with rational coefficients. In this case, you might need to use numerical methods or a graphing calculator to find approximate solutions. One common numerical method is the Newton-Raphson method, which can be used to approximate solutions for equations that cannot be easily solved algebraically.

   Alternatively, you can graph the equation $y = 4x^4 - 8x^3 + 6x^2 - 4x - 15$ and find the x-intercepts (where $y = 0$). There are several online graphing tools that can help you visualize the equation and find its roots.