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

Question

3277 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-04-10T02:57:29

#(42,41)#

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)#