GATE 2026 CE (CE1) – Question 28
It is given that $x$ and $y$ are integers in the following equation:
$$(x + y - 7)^2 + (y + 3x - 13)^2 = 0$$
The value of $(x^3 + y^3)$ is ______ (*in integer*).
Practise this question in The GATE Grind →
Show answer and explanation
Correct answer: 91
Explanation
A sum of two squares is zero only if both squares are zero. So $x + y = 7$ and $3x + y = 13$. Subtracting gives $2x = 6$, so $x = 3$ and $y = 4$. Then $x^3 + y^3 = 27 + 64 = 91$.