Question

Find two given numbers in a given ratio such that the sum of their squares is to their difference in a given ratio. Ratios being 3 : 1 and 10 : 1.

Answer 1

Answer: a=6 and b=2

Explanation:

Let say A and b the 2 numbers.

`(a)/(b) =(3)/(1) \Longrightarrow\ a=3b\\\\(a^2+b^2)/(a-b) =(10)/(1) \Longrightarrow\ (3b)^2+b^2=10*(3b-b)\\\\\Longrightarrow\ 10*b^2=10*2b\\\\\Longrightarrow\ b=2\\\\\Longrightarrow\ a=6\\\\`