How to Solve the Algebra Equation With Square Root?

Algebra equation with square roots
Solve the algebra equation with square root, when the math equation is √(x + √(x + 11)) + √(x – √(x + 11)) = 4
Solution to the algebra equation with square roots
We have
√(x + √(x + 11)) + √(x – √(x + 11)) = 4
Let, y = √(x + 11) then
√(x + √(x + 11)) + √(x – √(x + 11)) = 4
⇒ √(x + y) + √(x – y) = 4
⇒ √(x + y) = 4 – √(x – y)
Square both sides, then
x + y = 16 – 2 × 4 × √(x – y) + x – y
⇒ 2y – 16 = – 8√(x – y)
⇒ y – 8 = – 4√(x – y)
Square both sides again
y² – 16y + 64 = 16(x – y)
⇒ y² – 16y + 64 = 16x – 16y
⇒ y² + 64 = 16x
We know, y = √(x + 11) then
x + 11 + 64 = 16x
⇒ 15x = 65
⇒ x = 5
so solution to the algebra equation with square root is 5