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?
1 Answer
Jan 24, 2016
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
