Question

[Bạch mã hoàng tử]

Vận dụng tính chất dãy tỉ số bằng nhau:

a)Cho \(ac=b^2;ab=c^2;a+b+c\ne0;a,b,c\ne0\)

Tính:\(P=\frac{b^{333}}{a^{111}\cdot c^{222}}\)

b)Cho \(x^2=yz;y^2=xz;x+y+z\ne0;xyz\ne0\)

Answer 1

[Nguyễn Linh Chi]

a) \(ac=b^2\Rightarrow\frac{a}{b}=\frac{b}{c}\)

\(ab=c^2\Rightarrow\frac{a}{c}=\frac{c}{b}\)

Suy ra: \(\frac{a}{b}=\frac{b}{c}=\frac{c}{a}=\frac{a+b+c}{a+b+c}=1\)

\(P=\frac{b^{333}}{a^{111}.c^{222}}=\frac{b^{333}}{a^{111}.c^{111}.c^{111}}=\frac{b^{333}}{\left(ac\right)^{111}.c^{111}}=\frac{b^{333}}{\left(b^2\right)^{111}.c^{111}}=\frac{b^{333}}{b^{222}.c^{111}}=\frac{b^{111}}{c^{111}}=\left(\frac{b}{c}\right)^{111}\)

\(=1^{111}=1\)