SOLUTION: A positive number is three more than twice another number. Their product is 10 more than the square of the smaller number. Find the numbers.

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Question 54373: A positive number is three more than twice another number. Their product is 10 more than the square of the smaller number. Find the numbers.
Answer by anjulasahay(30) (Show Source):
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A positive number is three more than twice another number. Their product is 10 more than the square of the smaller number. Find the numbers.
ans:let the two numbers be x and y.
then according to the problem x = 2*y+3
it is clear from the above expression that x > y (it can be checked by putting y = 0,1,2...)
hence from the problem we can write that
x*y = y^2+10
(2*y+3)*y=y^2+10
2y^2+3y=y^2+10
y^2+3y-10=0
y^2+5y-2y-10=0
y(y+5)-2(y+5)=0
(y-2)(y+5) = 0
y = 2 or -5
and x = 7 or -7
hence hence the two numbers are either ( 7 and 2 ) or (-5 and -7)