43^2+58^2+62^2=?
1 Answer
Dec 20, 2015
Explanation:
Use:
43^2 = (40+3)^2 = 40^2 + 2*40*3 + 3^2 = 1600+240 + 9 = 1849
If we change the sign of
(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