Question

[✓ ℍɠŞ_ŦƦùM $₦G ✓]

Cho : \(\frac{x}{a}+\frac{y}{b}+\frac{z}{c}=1;\frac{a}{x}+\frac{b}{y}+\frac{c}{z}=0\left(a,b,c,x,y,z\ne0\right)\)

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

Answer 1

[Nhân Thiện Hoàng]

khó quá ta

Answer 2

[Nguyễn Anh Quân]

Đặt : x/a = m ; y/b = n ; z/c = p

=> m+n+p = 1 ; 1/m+1/n+1/p=0

1/m+1/n+1/p=0

<=> mn+np+pm/mnp=0

<=> mn+np+pm=0

<=> 2mn+2np+2pm=0

Xét : 1 = (m+n+p)^2 = m^2+n^2+p^2+2mn+2np+2pm = m^2+n^2+p^2

=> x^2/a^2+y^2/b^2+z^2/c^2 = 1

=> ĐPCM

Tk mk nha