Question

a+1/a=17/4 find (a-1/a)

Answer 1

Heya!!

Thanks for asking the question!

Answer : Either 15/4 or -15/4

Pls refer to the attachment for the solution.

Hope it helps you : )

Answer 2

$a - \frac{1}{a} = \frac{15}{4}$

Solution:

Given that,

$a+\frac{1}{a} = \frac{17}{4}$

To find: $a - \frac{1}{a}$

From given,

$a+\frac{1}{a} = \frac{17}{4}\\\\Take\ square\ on\ both\ sides\\\\(a+\frac{1}{a})^2 = (\frac{17}{4})^2\\\\Expanding\\\\a^2 + \frac{1}{a^2}+ 2 = \frac{289}{16}\\\\a^2 + \frac{1}{a^2} = \frac{289}{16}-2\\\\a^2 + \frac{1}{a^2} = \frac{289-32}{16}\\\\a^2 + \frac{1}{a^2} = \frac{257}{16} ------ eqn 1$

Now expand,

$a - \frac{1}{a}\\\\Take\ square\\\\(a-\frac{1}{a})^2 = a^2 + \frac{1}{a^2} - 2\\\\Substitute\ eqn\ 1\\\\(a-\frac{1}{a})^2 = \frac{257}{16} - 2\\\\(a-\frac{1}{a})^2 = \frac{257 - 32}{16}\\\\(a-\frac{1}{a})^2 = \frac{225}{16}\\\\Take\ square\ root\ on\ both\ sides\\\\a - \frac{1}{a} = \frac{15}{4}$

Thus the required is found

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