Question

Fie egalitatea (x+y+z)la puterea 2= x la puterea 2 + y la puterea 2 + z la puterea 2+ 2xy+2yz+2zx. Verficati egalitatea pentru: a) x=y=z=10; b) x=2; y=3; z=4.

Answer 1

a) x = y = z = 10

(x+y+z)^2 = (10+10+10)^2 = 30^2 = 900

(10+10+10)^2 = 10^2+10^2+10^2+2*10*10+2*10*10+2*10*10 = 100+100+100+200+200+200 = 900

b) x = 2, y = 3, z = 4

(x + y + z)^2 = (2+3+4)^2 = 9^2 = 81

(2+3+4)^2 = 2^2+3^2+4^2+2*2*3+2*3*4+2*4*2 = 4+9+16+12+24+16 = 81