The sum of the squares of two positive integers is 117. If the square of the smaller number equals four times the larger number,

Question

Represent the following situations mathematically:

The sum of the squares of two positive integers is 117. If the square of the smaller number equals four times the larger number, we need to find the integers.

Answer 1

Let ‘x’ and ‘y’ be the smaller and larger integer respectively.

∴ x² + y² = 117.

[∵ The sum of the squares of two positive integers is 117]

∴ x² = 4y

[∵ the square of the smaller number equals four times the larger number.]

∴ y² + 4y – 117 = 0