SOLUTION: find two consecutive positive intergers such that the square of the larger integer added to seven times the smaller integer is equal to 253?

SOLUTION: find two consecutive positive intergers such that the square of the larger integer added to seven times the smaller integer is equal to 253?

Algebra.Com

Question 370490: find two consecutive positive intergers such that the square of the larger integer added to seven times the smaller integer is equal to 253?
Answer by checkley77(12844) (Show Source): You can put this solution on YOUR website!
Let x & (x+1) be the 2 integers.
(x+1)^2+7x=253
x^2+2x+1+7x=253
x^2+9x+1-253=0
x^2+9x-252=0
(x-12)(x+21)=0
x-12=0
x=12 ANS FOR THE SMALLER INTEGER.
12+1=13 ANS. FOR THE LARGER INTEGER.
Proof:
13^2+7*12=253
169+84=253
253=253
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