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

1 Answer
Apr 10, 2018

Answer:

#(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)#