Question

The difference between the square of two numbers is 11. Twice the square of the first number increased by the square of the second number is 97 find the numbers

Answer 1

Below in bold.

Explanation:

x^2 - y^2 = 11

2x^2 + y^2 = 97

From the first equation:

y^2 = x^2 - 11

Substituting in the second equation:

2x^2 + x^2 - 11 = 97

3x^2 = 108

x^2 = 36

x = 6, -6.

Substituting for x in the first equation:

(6)^2 - y^2 = 11

y^2 = 36 - 11 = 25

y = 5, -5.