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

Step-by-step explanation:

Let say A and b the 2 numbers.

$\dfrac{a}{b} =\dfrac{3}{1} \Longrightarrow\ a=3b\\\\\dfrac{a^2+b^2}{a-b} =\dfrac{10}{1} \Longrightarrow\ (3b)^2+b^2=10*(3b-b)\\\\\Longrightarrow\ 10*b^2=10*2b\\\\\Longrightarrow\ b=2\\\\\Longrightarrow\ a=6$