Question

Cho tỉ lệ thức \(\frac{x}{z}\)=\(\frac{z}{y}\)Chứng minh rằng \(\frac{^{x^2}+z^2}{y^2+z^2}\)=\(\frac{x}{y}\)

Answer 1

Có\(\frac{x}{z}=\frac{z}{y}\)⇒\(xy=\text{x}^{2}\)

⇒\(\frac{\text{x}^{2}+\text{z}^{2}}{\text{y}^{2}+\text{z}^{2}}\)=\(\frac{\text{x}^{2}+xy}{\text{y}^{2}+xy}\)=\(\frac{x(x+y)}{y(x+y)}\)=\(\frac{x}{y}\)

⇒\(\frac{\text{x}^{2}+\text{z}^{2}}{\text{y}^{2}+\text{z}^{2}}\)=\(\frac{x}{y}\)

Vậy \(\frac{\text{x}^{2}+\text{z}^{2}}{\text{y}^{2}+\text{z}^{2}}\)=\(\frac{x}{y}\)

Answer 2

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