One number is 1 more than another number. The sum of their squares is 181. Find the numbers.
A)9, 10 or -10, -9
B)2, 3 or -3, -2
C)5, 6 or -6, -5
D)6, 7 or -7, -6
E)7, 8 or -8, -7

Question

Quizplus · Accepted Answer

Let the two numbers be x and x+1. Their squares are $x^2$ and $(x+1)^2$. The equation is $x^2 + (x+1)^2 = 181$. Simplifying gives $2x^2 + 2x - 180 = 0$, which simplifies to $x^2 + x - 90 = 0$. Factoring gives $(x-9)(x+10) = 0$, so $x = 9$ or $x = -10$. Thus, the pairs are (9, 10) and (-10, -9).

One Number Is 1 More Than Another Number