Question

If a+1/a =17/4 find the value of (a-1/a)
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Answer 1

$let \: a \: = x \\ \\ x + \frac{1}{x} = \frac{17}{4} \\ \\ sobs \\ \\ {x}^{2} + \frac{1}{ {x}^{2} } + 2 = \frac{289}{16} \\ \\ {x}^{2} + \frac{1}{ {x}^{2} } = \frac{257}{16} \\ \\ {x}^{2} + \frac{1}{ {x}^{2} } - 2 = \frac{225}{16} \\ \\ (x - \frac{1}{x} ) {}^{2} = {( \frac{15}{4} )}^{2} \\ \\ x - \frac{1}{x} = \frac{15}{4} \\ \\ a - \frac{1}{a} = \frac{15}{4}$

hope it helps

Answer 2

Answer:

9root5/4

Step-by-step explanation:

a+1/a=17/4

(a+1/a)2=(17/4)2

a2+1/a2+2=289/16

a2+1/a2=289/16-2

(a-1/a)2=a2+1/a2-2

(a-1/a)2=289/16-2-2

(a-1/a)2=289/16-4

(a-1/a)2=225/16

a-1/a=9root5/4