Question

Let $x$ and $y$ be positive integers such that $x^2 + y^2 + xy = 61$. If $x = 4$, then the value of $y$ is

• A. 4
• B. 5
• C. 6
• D. 7

Hint:

After substitution, simplify to a quadratic and factorize for integer solutions.

Answer 1

The Correct Option is B

Concept: Substitute the given value and solve the quadratic equation. Explanation: Given $x = 4$ \[ 4^2 + y^2 + 4y = 61 \] \[ 16 + y^2 + 4y = 61 \] \[ y^2 + 4y - 45 = 0 \] Factorizing: \[ (y + 9)(y - 5) = 0 \] Since $y$ is positive, $y = 5$.