The difference of two positive whole numbers in 3 and the sum of their squars is 117. Find the two numbers.

Explanation

Let one of the numbers=x,
`:.` the other number =(x-3)or(x+3)
As per question, `x^(2)+(x-3)^(2)=117" "and" "x^(2)+(x+3)^(2)=117`
or, `x^(2)+x^(2)-6x+9=177or,x^(2)+x^(2)+6x+9=117`
or, `2x^(2)-6x+9-117=0" "or,2x^(2)+6x+9-117=0`
or, `2x^(2)-6x-108=0" "or,2x^(2)+6x-108=0`
or, `x^(2)-3x-54=0" "or,x^(2)+3x-54=0`
or, `x^(2)-(9-6)x-54=0" "or,x^(2)+(9-6)x-54=0`
or, `x^(2)-9x+6x-54=0" "or,x^(2)+9x-6x-54=0`
or, `x(x-9)+6(x-9)=0" "or,x(x+9)-6(x+9)=0`
or, `(x-9)(x+6)=0" "or,(x+9)(x-6)=0`
`:.` either x-`x-9=0or,x+6=0" ""either "x+9=0or,x=6`
`impliesx=9or,x=-6" "impliesx=-9or,x=6`
`:'` x is positive, `:.xne-6" ":'x` is positive `:.xne-9`.
Hence the required two numbers are 6 and 9.