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

1 Answer
George C.
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#

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