Question

√(x+2)+√(2x-1)=-2 √(x^2-9)=3x-11

Answer 1

Держи ответ на вопрос)

Answer 2

To solve the given system of equations:

Equation 1: √(x+2) + √(2x-1) = -2 Equation 2: √(x^2-9) = 3x - 11

Let's solve them one by one.

Equation 1: We can start by isolating one of the radicals and then square both sides to eliminate the square roots.

√(x+2) + √(2x-1) = -2

Subtracting √(x+2) from both sides: √(2x-1) = -2 - √(x+2)

Now, square both sides of the equation to eliminate the square root: (√(2x-1))^2 = (-2 - √(x+2))^2 2x - 1 = 4 + 4√(x+2) + (x + 2) 2x - 1 = x + 6 + 4√(x+2)

Rearranging terms: x - 7 = 4√(x+2)

Now, square both sides again to eliminate the square root: (x - 7)^2 = (4√(x+2))^2 x^2 - 14x + 49 = 16(x + 2) x^2 - 14x + 49 = 16x + 32

Simplifying the equation: x^2 - 14x - 16x + 49 - 32 = 0 x^2 - 30x + 17 = 0

We can solve this quadratic equation using the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / (2a)

For our equation, a = 1, b = -30, and c = 17. Substituting these values:

x = (-(-30) ± √((-30)^2 - 4117)) / (2*1) x = (30 ± √(900 - 68)) / 2 x = (30 ± √832) / 2 x = (30 ± √(16 * 52)) / 2 x = (30 ± 4√13) / 2 x = 15 ± 2√13

So we have two possible solutions for x: x₁ = 15 + 2√13 and x₂ = 15 - 2√13.

Now let's solve Equation 2:

Equation 2: √(x^2-9) = 3x - 11

To eliminate the square root, we can square both sides of the equation:

(√(x^2-9))^2 = (3x - 11)^2 x^2 - 9 = 9x^2 - 66x + 121

Rearranging terms: 8x^2 - 66x + 130 = 0

We can solve this quadratic equation using the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / (2a)

For our equation, a = 8, b = -66, and c = 130. Substituting these values:

x = (-(-66) ± √((-66)^2 - 48130)) / (2*8) x = (66 ± √(4356 - 4160)) / 16 x = (66 ± √196) / 16 x