Sum of a fraction and thrice of its reciprocal is 73/20. What is the fraction?
5/4
Let the fraction be \(x\). Then \(x + \dfrac{3}{x} = \dfrac{73}{20}\).
Multiplying by \(20x\):
\[20x^2 - 73x + 60 = 0\]
Factoring: \((4x - 5)(5x - 12) = 0\), giving \(x = \dfrac{5}{4}\) or \(x = \dfrac{12}{5}\).
Among the options, only 5/4 appears. Check: \(\dfrac{5}{4} + 3 \cdot \dfrac{4}{5} = \dfrac{25}{20} + \dfrac{48}{20} = \dfrac{73}{20}\). ✓
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Important Questions from Quadratic Equation
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If the roots of the equation (q – r)x 2+ (r – p)x + (p – q) = 0 are equal, then which of the following is true?
Number of real roots of the quadratic equation 3x 2+ 4x + 25 = 0 is
The value of m for which one of the root of x 2 - 3x + 2m = 0 is double of the root of x 2 - x + m = 0 is:
If x 2+ 1 = 2x, then find x – \((\frac{1}{x})\)
