Question 115
If $$\frac{3-5x}{x} + \frac{3-5y}{y} + \frac{3-5z}{z} = 0 $$, the value of $$\frac{1}{x} + \frac{1}{y} + \frac{1}{z}$$ is
Solution
Expression : $$\frac{3-5x}{x} + \frac{3-5y}{y} + \frac{3-5z}{z} = 0 $$
=> $$\frac{3}{x} - \frac{5x}{x} + \frac{3}{y} - \frac{5y}{y} + \frac{3}{z} - \frac{5z}{z} = 0$$
=> $$\frac{3}{x} + \frac{3}{y} + \frac{3}{z} - 15 = 0$$
=> $$3 (\frac{1}{x} + \frac{1}{y} + \frac{1}{z}) = 15$$
=> $$\frac{1}{x} + \frac{1}{y} + \frac{1}{z} = \frac{15}{3} = 5$$
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