√11-x^2+√5-x^2=2

To solve this equation, we first need to isolate the square root terms on one side of the equation.

√11 - x^2 + √5 - x^2 = 2

Combine the square root terms:

√11 + √5 - 2x^2 = 2

Now, isolate the square root terms on one side:

√11 + √5 = 2 + 2x^2

Subtract 2 from both sides:

√11 + √5 - 2 = 2x^2

Now, square both sides to eliminate the square roots:

(√11 + √5 - 2)^2 = (2x^2)^2

(√11 + √5 - 2)(√11 + √5 - 2) = 4x^4

Expanding the left side:

11 + 5 + 4√55 - 4√11 - 2√5 - 2√5 = 4x^4

16 + 4√55 - 4√11 - 4√5 = 4x^4

Now, divide by 4 to simplify:

4 + √55 - √11 - √5 = x^4

Therefore, the solution to the equation is x = ±√(4 + √55 - √11 - √5).