Question

\sqrt{-2x^{2}-2x+11 }=\sqrt{-x^{2} +3}

Answer 1

Explanation:

sqrt{-2x^{2}-2x+11 }=\sqrt{-x^{2} +3}

Square both sides:

-2x^2 - 2x + 11 = -x^2 + 3

0 = x^2 + 2x - 8

( x + 4)(x - 2) = 0

x = -4, 2.

As the original equation contains square roots some of these roots might be extraneous.

Checking:

x = -4

sqrt(-2(-4)^2 - 2(-4) + 11 = sqrt(-13)

sqrt (-(-4)^2 + 3) = sqrt(-13)

x = 2:

sqrt(-2(4) - 2(2) + 11) = sqrt(-8 - 4 + 11) = sqrt(-1)

sqrt(-(2)^2 + 3) = sqrt(-1)

So both are roots