Question

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

Answer 1

Ответ:

Пошаговое объяснение:

x²-2+x²-6x+9=2x²

7-6x=0

-6x=-7

x = 7/6

Answer 2

Let's solve the equation step by step.

Starting with the given equation:

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

Expanding the square of (x - 3):

(x^2 - 2) + (x^2 - 6x + 9) = 2x^2

Combine like terms:

x^2 - 2 + x^2 - 6x + 9 = 2x^2

Rearrange the terms:

2x^2 - 2 - x^2 + 6x - 9 = 0

Combine like terms:

x^2 + 6x - 11 = 0

Now, we have a quadratic equation in standard form. We can solve it using the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / (2a)

For our equation, a = 1, b = 6, and c = -11. Substituting these values into the formula:

x = (-6 ± √(6^2 - 4(1)(-11))) / (2(1))

Simplifying further:

x = (-6 ± √(36 + 44)) / 2

x = (-6 ± √80) / 2

x = (-6 ± √(16 * 5)) / 2

x = (-6 ± 4√5) / 2

Simplifying the expression:

x = -3 ± 2√5

Therefore, the solutions to the equation (x^2 - 2) + (x - 3)^2 = 2x^2 are:

x = -3 + 2√5 x = -3 - 2√5