2022 · Q10
If (x + √(1 + x²))(y + √(1 + y²)) = 1, where x and y are real numbers, then what is the value of (x + y)²?
Elementary MathematicsAlgebra
- A0
- B1
- C4
- D9
Explanation
Since (√(1+x²)-x)(√(1+x²)+x) = 1, the given equation gives y+√(1+y²) = √(1+x²)-x. The function f(t) = t+√(1+t²) is strictly increasing (its derivative exceeds 0), hence injective, so y = -x. Therefore (x+y)² = 0. Hence the keyed option is A.