If x+1x=174,x>1x + \frac {1}{x}= \frac{17}{4}, x > 1x+x1=417,x>1, then what is the value of x−1xx-\frac{1}{x}x−x1? A83\frac8338 B154\frac{15}{4}415 C23\frac2332 D94\frac94 49 Show answer & explanationCorrect answer: BExplanationThe correct answer is Option 2 i.e 154\frac{15}{4}415. (x+1x)2=(174)2(x + \frac {1}{x})^2= (\frac{17}{4})^2(x+x1)2=(417)2 2 subtracted from both sides. ⇒ x2+1x2+2−2=28916−2x^2 + \frac {1}{x^2}+2-2= \frac{289}{16}-2x2+x21+2−2=16289−2 ⇒ (x−1x)2+2=(25716)(x - \frac {1}{x})^2+2= (\frac{257}{16})(x−x1)2+2=(16257) ⇒ (x−1x)2=(25716)−2(x - \frac {1}{x})^2= (\frac{257}{16})-2(x−x1)2=(16257)−2 ⇒ (x−1x)2=(22516)(x - \frac {1}{x})^2= (\frac{225}{16})(x−x1)2=(16225) ⇒ x−1x=154x - \frac {1}{x}= \frac{15}{4}x−x1=415