2022 · Q15
If x² = 17x + y and y² = x + 17y, x ≠ y, then what is the value of √(x²+y²+1)?
Elementary MathematicsAlgebra
- A17
- B19
- C23
- D27
Explanation
Subtracting the equations: x²-y² = 16(x-y), and since x≠y, x+y = 16. Adding them: x²+y² = 18(x+y) = 288. Thus √(x²+y²+1) = √289 = 17. Hence the keyed option is A.