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√{ y + √(2xy - x²)} + √{y -√(2xy - x²) = √(2x)take square of both sides ,
[√{y + (2xy -x²)} + √{y -√(2xy - x²)}]² =(√(2x))²
y + √(2xy - x²) + y - √(2xy - x²) + 2√{y - √(2xy - x²)}√{y + √(2xy - x²)} = 2x
2y + 2√{ y² - (√(2xy - x²))2 } = 2x
2y + 2√(y² - 2xy + x²) = 2x
2y + 2√(x - y)² = 2x
2y + 2| (x - y)| = 2x
but question ask x > y
so, |(x - y)| = (x - y)
2y + 2(x - y) = 2x
2y + 2x -2y = 2x
2x = 2x
LHS = RHS