Question

Tính giá trị biểu thức :

M= x^2/a^2 + y^2/b^2+ z^2/c^2 nếu x/a+y/b+z/c=1 và a/+b/y+c/z = 0

Answer 1

Từ \(\frac{a}{x}+\frac{b}{y}+\frac{c}{z}=0=>\frac{ayz}{xyz}+\frac{bxz}{xyz}+\frac{cxy}{xyz}=0=>\frac{ayz+bxz+cxy}{xyz}=0=>ayz+bxz+cxy=0\)

Từ \(\frac{x}{a}+\frac{y}{b}+\frac{z}{c}=1=>\left(\frac{x}{a}+\frac{y}{b}+\frac{z}{c}\right)^2=1^2\)

\(=>\frac{x^2}{a^2}+\frac{y^2}{b^2}+\frac{z^2}{c^2}+2\left(\frac{xy}{ab}+\frac{yz}{bc}+\frac{xz}{ac}\right)=1\)

\(=>\frac{x^2}{a^2}+\frac{y^2}{b^2}+\frac{z^2}{c^2}=1-2\left(\frac{xyc}{abc}+\frac{yza}{abc}+\frac{xzb}{abc}\right)=1-2.0=1\)

Vậy M=1