Question

a+1/a=17/4 ,find a-1/a

Answer 1

a+1/a=17/4
Cross Multiplying,We Get

4a+4=17a

17a-4a=4

13a=4

a=4/13

a-1/a ............eq.1

putting value of "a" in eq.1
we get,
(4/13 -1)/4/13

(4-13/13) / 4/13

Ans..-9/4

Answer 2

Answer:

$\dfrac{15}{4}$

Step-by-step explanation:

$\sf \: a + \dfrac{1}{a} = \dfrac{17}{4}$

[Squaring Both Sides]

$\sf(a + \dfrac{1}{a} ) ^{2} = (\dfrac{17}{4} )^{2}$

$\sf {a}^{2} + \dfrac{1}{ {a}^{2} } + 2(a)( \dfrac{1}{a} ) = \dfrac{289}{16}$

[Subtracting 4 from both sides]

$\sf{a}^{2} + \dfrac{1}{ {a}^{2} } + 2 - 4 = \dfrac{289 - 64}{16}$

$\sf {a}^{2} + \dfrac{1}{ {a}^{2} } - 2 = \dfrac{225}{16}$

$\sf {a}^{2} + (\dfrac{1}{ {a} } )^{2} - 2(a)( \dfrac{1}{a}) = (\dfrac{15}{4} )^{2}$

$\sf \: a - \dfrac{1}{a} = \dfrac{15}{4}$