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InterviewSolution
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If \(\frac{1}{{x + \frac{1}{{y + \frac{2}{{z + \frac{1}{4}}}}}}} = \frac{{29}}{{79}}\) where x, y, and z are natural numbers, then the value of (2x + 3y - z) is:1. 42. 03. 24. 1 |
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Answer» Correct Answer - Option 3 : 2 Given: \(\frac{1}{{x + \frac{1}{{y + \frac{2}{{z + \frac{1}{4}}}}}}} = \frac{{29}}{{79}}\) Calculation: RHS can be written as: \(⇒ \;\frac{1}{{\frac{{79}}{{29}}}} = \frac{{29}}{{79}}\) \( ⇒ \;\frac{1}{{2\; +\ \frac{{21}}{{29}}\;}} = \frac{{29}}{{79}}\) \(⇒ \;\frac{1}{{2\; +\ \frac{1}{{\frac{{21}}{{29}}}}\;}} = \frac{{29}}{{79}}\) \(⇒ \;\frac{1}{{2\; +\ \frac{1}{{1 \ +\ \frac{8}{{21}}}}\;}} = \frac{{29}}{{79}}\) \(⇒ \;\frac{1}{{2\; +\ \frac{1}{{1\ +\ \frac{2}{{\frac{{21}}{4}}}}}\;}} = \frac{{29}}{{79}}\) \(⇒ \;\frac{1}{{2\; +\ \frac{1}{{1\ +\ \frac{2}{{5\ +\ \frac{1}{4}}}}}\;}} = \frac{{29}}{{79}}\) After comparing LHS with the question, x = 2, y = 1, z = 5 Substituting the value of x, y and z in (2x + 3y - z), ⇒ 2(2) + 3(1) - 5 ⇒ 4 + 3 - 5 ⇒ 2 ∴ The value of (2x + 3y - z) is 2. |
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