43^2+58^2+62^2=?

1 Answer
Dec 20, 2015

9057

Explanation:

Use: (a+b)^2 = a^2+2ab+b^2

43^2 = (40+3)^2 = 40^2 + 2*40*3 + 3^2 = 1600+240 + 9 = 1849

If we change the sign of b we get:

(a-b)^2 = a^2-2ab+b^2

So, in combination:

(a-b)^2 + (a+b)^2 = a^2-color(red)(cancel(color(black)(2ab)))+b^2+a^2+color(red)(cancel(color(black)(2ab)))+b^2

=2a^2+2b^2

For example:

58^2+62^2 = (60-2)^2 + (60+2)^2

=60^2-color(red)(cancel(color(black)(2*60*2)))+2^2 + 60^2+color(red)(cancel(color(black)(2*60*2)))+2^2

=2*60^2 + 2*2^2 = 7200+8 = 7208

So:

43^2+58^2+62^2 = 1849+7208 = 9057