Question

(x+1)(x-1)+(x+2)(x-2)=2(1-x)(x-2)

Answer 1

Объяснение:

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Answer 2

Объяснение:

$\displaystyle\\(x+1)*(x-1)+(x+2)*(x-2)=2*(1-x)*(x-2)\\\\x^2-1^2+x^2-2^2=2*(x-x^2-2+2x)\\\\2x^2-1-4=2*(-x^2+3x-2)\\\\2x^2-5=-2x^2+6x-4\\\\4x^2-6x-1=0\\\\x_{1,2}=\frac{-(-6)б\sqrt{(-6)^2-4*4*(-1)} }{2*4} =\frac{6б\sqrt{36+16} }{8}=\frac{6б\sqrt{52} }{8}= \frac{6б\sqrt{4*13} }{8}\\\\=\frac{6б2\sqrt{13} }{8}=\frac{3б\sqrt{13} }{4} \\\\ x_1=\frac{3+\sqrt{13} }{4}\approx1,6514.\\\\x_2=\frac{3-\sqrt{13} }{4} \approx-0,1514.$

Answer 3

To solve the equation (x+1)(x-1) + (x+2)(x-2) = 2(1-x)(x-2), you can start by expanding the expressions on both sides and then simplifying the equation.

Let's expand and simplify each side step by step:

Left side: (x+1)(x-1) + (x+2)(x-2) = x(x-1) + 1(x-1) + x(x-2) + 2(x-2) = x^2 - x + x - 1 + x^2 - 2x + 2x - 4

Combine like terms: x^2 + x^2 - x + x - 2x + 2x - 1 - 4

Now, simplify further: 2x^2 - 5

Right side: 2(1-x)(x-2) = 2(1x - 2 - x^2 + 2x) = 2x - 4 - 2x^2 + 4x

Combine like terms: 2x - 2x^2

Now, the equation becomes: 2x^2 - 5 = 2x - 2x^2

Now, you can move all the terms to one side of the equation:

2x^2 - 2x^2 - 2x + 5 = 0

Simplify: -2x + 5 = 0

Now, solve for x: -2x = -5

Divide by -2 to isolate x: x = -5 / -2

x = 5/2

So, the solution to the equation is x = 5/2.