Question

(x - 2)² + (x- 3 ) ² = 2x²​

Answer 1

x²-4x+4+x²-6x+9=2x²

-10x+13=0

x= 1,3

Answer 2

Let's solve the given equation:

(x - 2)² + (x - 3)² = 2x²

Step 1: Expand the squares (x - 2)(x - 2) + (x - 3)(x - 3) = 2x² (x² - 4x + 4) + (x² - 6x + 9) = 2x²

Step 2: Combine like terms on the left side x² - 4x + 4 + x² - 6x + 9 = 2x²

Step 3: Move all terms to one side of the equation x² - 4x + 4 + x² - 6x + 9 - 2x² = 0

Step 4: Simplify the equation x² - 4x + x² - 6x + 13 = 0

Step 5: Combine like terms 2x² - 10x + 13 = 0

Now, we have a quadratic equation in standard form (ax² + bx + c = 0), where: a = 2 b = -10 c = 13

Step 6: Use the quadratic formula to find the values of x:

The quadratic formula is given by: x = (-b ± √(b² - 4ac)) / 2a

Plugging in the values: x = (10 ± √((-10)² - 4 * 2 * 13)) / 2 * 2 x = (10 ± √(100 - 104)) / 4 x = (10 ± √(-4)) / 4

Since the square root of a negative number is imaginary, there are no real solutions for x in this equation. The graph of the equation is a pair of imaginary points on the x-axis.