Question

(x-3)^2+(x+2)^2=2(3-x)(x+2)

Answer 1

(x-3)²+(x+2)²=2(3-x)(x+2)

Решение:

x²-6x+9+x²+4x+4=(6-2x)*(x+2)

2x²-2x+13=6x+12-2x²-4x

2x²-2x+13-2x-12+2x²=0

4x²-4x+1=0

x=$\frac{4+-\sqrt{16-16} }{8}$

x=$\frac{4}{8}$

x=$\frac{1}{2}$

Ответ: x=$\frac{1}{2}$

Answer 2

Ответ:

Объяснение:

(x-3)²+(x+2)²=2(3-x)(x+2)

(x-3)²+(x+2)²=-2(x-3)(x+2)

(x-3)²+2(x-3)(x+2)+(x+2)^2=0

(x-3)²+(x-3)(x+2)+(x-3)(x+2)+(x+2)²=0

(x-3)[(x-3)+(x+2)] + (x+2)[(x-3)+(x+2)]=0

(x-3)(2x-1) + (x+2)(2x-1)=0

(2x-1)[(x-3)+(x+2)]=0

(2x-1)(2x-1)=0

2x-1=0

2x=1

x=1/2

Answer 3

To solve the given equation, let's start by expanding and simplifying both sides step by step:

Step 1: Expand the squares on both sides of the equation. (x - 3)^2 + (x + 2)^2 = 2(3 - x)(x + 2)

Expanding the squares: (x - 3)(x - 3) + (x + 2)(x + 2) = 2(3 - x)(x + 2)

Step 2: Simplify both sides further. (x^2 - 6x + 9) + (x^2 + 4x + 4) = 2(3x + 6 - x^2 - 2x)

Step 3: Combine like terms on both sides. x^2 - 6x + 9 + x^2 + 4x + 4 = 6x + 12 - 2x^2 - 4x

Step 4: Collect like terms on one side to get the quadratic equation in standard form. 2x^2 - 6x + 13 = 6x + 12 - 2x^2 - 4x

Step 5: Move all terms to one side to form a quadratic equation equal to zero. 2x^2 - 6x + 13 - 6x - 12 + 2x^2 + 4x = 0

Step 6: Combine like terms again. 4x^2 - 10x + 1 = 0

Now, we have a quadratic equation in the form ax^2 + bx + c = 0, where: a = 4 b = -10 c = 1

To solve this quadratic equation, we can use the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / 2a

Plugging in the values, we get:

x = (10 ± √((-10)^2 - 4 * 4 * 1)) / (2 * 4) x = (10 ± √(100 - 16)) / 8 x = (10 ± √84) / 8 x = (10 ± √(4 * 21)) / 8 x = (10 ± 2√21) / 8

Now, we can find two solutions for x:

1. x = (10 + 2√21) / 8
2. x = (10 - 2√21) / 8

These are the two solutions for the given equation.