Question

[Phạm Minh Tuấn]

Cho \(\frac{x}{a}+\frac{y}{b}+\frac{z}{c}=1,\frac{a}{z}+\frac{b}{y}+\frac{c}{z}=0\)

Cmr: \(\frac{x^2}{a^2}+\frac{y^2}{b^2}+\frac{c^2}{z^2}=1\)

Answer 1

[Ly Ly]

• 1² = (x/a+y/b+z/c)² = (x/a)² + (y/b)² + (z/c)² +2(xy/ab+yz/bc+xz/ac) = (x/a)² + (y/b)² + (z/c)² +2[(cxy + ayz+bxz)/abc] (1)
• a/x + b/y + c/z = (ayz+bxz+cxy)/xyz = 0 

           Vì xyz khác 0 nên ayz+bxz+cxy=0 (2) 

•  Thế (2) vào (1) ta được x²/a² + y²/b² + z²/c² + 2(0/abc) = x²/a² + y²/b² + z²/c²  = 1 ( đpcm ) 

Answer 2

[Duy An]

1 nha anh !