#48^2+53^2+62^2=#?

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Answer 1 · 2015-12-25T00:16:35

#8957#

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

#48^2 = (50-2)^2 = 50^2-2(50)(2)+2^2#

#= 2500-200+4 = color(blue)(2304)#

#53^2 = (50+3)^2 = 50^2+2(50)(3)+3^2#

#=2500+300+9 = color(blue)(2809)#

#62^2 = (50+12)^2 = 50^2+2(50)(12)+12^2#

#=2500+1200+144 = color(blue)(3844)#

So:

#48^2+53^2+62^2 = 2304+2809+3844 = 8957#