Practicing Success
If xyz = 1, x + \(\frac{1}{y}\) = 5, y + \(\frac{1}{x}\) = 29 find (z + \(\frac{1}{y}\)) |
\(\frac{1}{3}\) \(\frac{1}{4}\) \(\frac{1}{6}\) 4 |
\(\frac{1}{4}\) |
Note the result: if x + \(\frac{1}{y}\) = m y + \(\frac{1}{z}\) = n z + \(\frac{1}{x}\) = p then (m×n×p) - (m+n+p) = xyz + \(\frac{1}{xyz}\) So, ATQ, m = 5 and n = 29, xyz = 1, put these values in result: (5 × 29 × p) - (5 + 29 + p) = xyz + \(\frac{1}{xyz}\) 145 p - (34 + p) = xyz + \(\frac{1}{xyz}\) 145 p - 34 - p = 1+1 145 p - p = 36 p (145 - 1) = 36 p = \(\frac{36}{144}\) p = \(\frac{1}{4}\) |