One number is 2 more than 2 times another. Their product is 2 more than 2 times their sum, how do you find the two integers?

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Answer 1 · 2015-07-05T09:16:22

Let's call the smaller number #x#.
Then the other number will be #2x+2#

Sum: #S=x+(2x+2)=3x+2#
Product: #P=x*(2x+2)=2x^2+2x#

#P=2*S+2#

Substituting:
#2x^2+2x=2*(3x+2)+2=6x+4+2#

Everything to one side:
#2x^2-4x-6=0-># divide everything by #2#
#x^2-2x-3=0-># factorise:
#(x-3)(x+1)=0->x=-1orx=3#

If we use the #2x+2# for the other number, we get the pairs:
#(-1,0)and(3,8)#