exo

bonsoir
on a : 1/x+1/y+1/z=0
montrez que (x+y+z)²=x²+y²+z²
merci beacoup!

on a (x+y+z)²=x²+y²+z²+2(xy+yz+xz)
càd
(x+y+z)²-x²+y²+z²=2(xy+yz+xz)

[(x+y+z)²-x²+y²+z²]/xyz = 2(xy+yz+xz)/xyz

[(x+y+z)²-x²+y²+z²]/xyz = 2( 1/x+1/y+1/z)=0
d'ou
[(x+y+z)²-x²+y²+z²]=0
càd
(x+y+z)²=x²+y²+z²