Question

numbers are in the ratio of 2 is to 3 and the difference of their squares is 320 find the numbers

Answer 1

let the numbers be 2x,3x
difference of squares=320...
that means (2x)2-(3x)2=320
=>4x2-9x2=320
=>-5x2=320
=>x2=320/5
x=√64
x=8
therefore numbers are 2×8=16...
3×8=24... answer is 16,24

Answer 2

one no =3x
another no =2x
a/q,
(3x) square-(2x) square
(3x+2x) (3x-2x)
=5x×x
=5xsqure=320
xsquare 64
x=8
no =24,16