Question

find the two consecutive numbers whose product exceeds the square of the smaller number by 7

Answer 1

Let 
Smaller integer = x
Greater integer= x+1
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Given
x*(x+1)=x^2+7
x*(x+1)=x^2+7
x^2+x=x^2+7
x^2-x^2+x=7
x=7
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Smaller integer = x =7
Greater = x+1 = 7+1=8
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Check
8*7=7^2+7
56=49+7
56=56

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