Question

difference between two positive numbers is 5 and the sum of theirs squares is 73 find the product of these numbers

Answer 1

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Answer 2

let the two numbers be x&y
then according to question
x-y=5------>(1)
x²+y²=73------->(2)
from (1) we get
x=5+y---------->(3)
putting value of equation (3) in equation (2) we get
(5+y)²+y²=73
5²+2(5)(y)+y²+y²=73
25+10y+y²+y²=73
10y+2y²=73-25
10y+2y²=48
2y²+10y-48=0
dividing whole equation by 2 we get
y²+5y-24=0
y²+8y-3y-24=0
y(y+8)-3(y+8)=0
(y-3)(y+8)=0
y-3=0 and y+8=0
y=3or-8
putting both values of y in equation (3) one by one we get
x=5+3=8
x=5-8=-3
x=-3or8
product of number =xy
xy =(3)(-3)=-9
xy=(8)(-8)=64
therefore both are possible answer