The difference between two positive numbers is 5 and the sum of their squares is 73 Find the - Maths - Expansions

Question

The difference between two positive numbers is 5 and the sum of
their squares is 73 Find the product of these numbers

Neha Sethi · Accepted Answer

Dear student
Let the two numbers be x and y,Then, Acc to question,x-y=5⇒x=y+5   
(1)and x2+y2=73y+52+y2=73⇒y2+25+10y+y2=73     As a+b2=a2+b2+2ab⇒2y2+10y-48=0⇒y2+5y-24=0⇒y2-3y+8y-24=0⇒y(y-3)+8(y-3)=0⇒(y+8)(y-3)=0⇒y+8=0 or y-3=0⇒y=-8 or y=3When y=-8 then x=-8+5=-3 then xy=(-3)(-8)=24When y=3 then x=3+5=8  then xy=(8)(3)=24
Regards

The difference between two positive numbers is 5 and the sum of their squares is 73 . Find the product of these numbers.