Question : If $\frac{3–5x}{2x}+\frac{3–5y}{2y}+\frac{3–5z}{2z}=0$, the value of $\frac{2}{x}+\frac{2}{y}+\frac{2}{z}$ is:
Option 1: 20
Option 2: 5
Option 3: 10
Option 4: 15
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Correct Answer: 10
Solution :
Given: $\frac{3–5x}{2x}+\frac{3–5y}{2y}+\frac{3–5z}{2z}=0$
⇒ $\frac{3}{2x}–\frac{5x}{2x}+\frac{3}{2y}–\frac{5y}{2y}+\frac{3}{2z}–\frac{5z}{2z}=0$
⇒ $\frac{3}{2x}+\frac{3}{2y}+\frac{3}{2z}–\frac{5x}{2x}–\frac{5y}{2y}–\frac{5z}{2z}=0$
⇒ $\frac{3}{2}(\frac{1}{x}+\frac{1}{y}+\frac{1}{z})–\frac{5}{2}–\frac{5}{2}–\frac{5}{2}=0$
⇒ $\frac{3}{2}(\frac{1}{x}+\frac{1}{y}+\frac{1}{z})=\frac{5}{2}+\frac{5}{2}+\frac{5}{2}$
⇒ $(\frac{1}{x}+\frac{1}{y}+\frac{1}{z})=\frac{15}{2}×\frac{2}{3}$
⇒ $2(\frac{1}{x}+\frac{1}{y}+\frac{1}{z})=\frac{15}{2}×\frac{2}{3}×2$
⇒ $\frac{2}{x}+\frac{2}{y}+\frac{2}{z}=10$
Hence, the correct answer is 10.
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