How do you find two consecutive positive integers if the sum of their squares is 3445?

1 Answer
Apr 10, 2018

(42,41)

Explanation:

First, translate the words into an equation:

x^2+y^2=3445

Since you know that x and y are consecutive, you know that one of the variables is larger by 1 compared to the other.

x=y-1

Via substitution, you get the new equation

x^2+(x-1)^2=3445

Expand the second term on the left-hand side

x^2+x^2-2x+1=3445

Simplification gets you a quadratic equation 2x^2-2x-3444=0.

This can be factored into 2(x-42)(x+41)

By the zero product rule, x=42, x=-41

Since they are positive integers, x=42

Because they are consecutive and x is larger than y, y=41

The final answer is (42,41)