Question

One number is 5 greater than another number.If the sum of their squares is 5 times the square of the smaller number,what are the numbers?

Answer 1

5 and 10

Explanation:

let the smaller number be n, then the 2nd will be n + 5

then : `n^2 + (n + 5 )^2 = 5n^2`

so `n^2 + n^2 + 10n + 25 = 5n^2`

and `3n^2 - 10n - 25 = 0`

To factor : `3 xx (-25) = -75`

(require factors of (-75) that also sum to (-10) )

These are 5 and - 15 : now rewrite equation as

# 3n^2 - 15n + 5n - 25 = 0 and factoring gives

3n(n - 5 ) + 5 (n - 5 ) = 0 so (n - 5 )(3n + 5 ) = 0

`rArr n = 5 or n = -5/3`

but n cannot be negative and hence n = 5 and n + 5 = 10