Question

The sum of the squares of two positive numbers is 53 and the difference of the squares of the numbers is 45. How do you find the number?

Answer 1

`7,2`

Explanation:

Let the two numbers be `a and b`, repectively.

`=> a^2+b^2=53 ---- (1)`
`=> a^2-b^2=45 ----(2)`

`(1)+(2) => 2a^2=98`
`=> a^2=49`
`=> a=+-7`
`=> b=+-2`

Given that `a` and `b` are both positive,
hence, `a=7, b=2`

Check :

`7^2+2^2=49+4=53`
`7^2-2^2=49-4=45`