Math, asked by Apurva77, 1 year ago

If
a  +  \frac{1}{a}  =  \frac{17}{4}
Find the value of
(a -  \frac{1}{a} )
First correct answer will be marked as brainliest..!!!

Answers

Answered by Anonymous
5
                           _________________

Given,

⇒ a + ( 1/a ) = 17/4.

Now,

⇒ { a - ( 1/a ) }² = { a + ( 1/a ) }² - 4 × a × 1/ a

⇒ { a - ( 1/a ) }² = ( 17/4 )² - 4

⇒ { a - ( 1/a ) }² = ( 289 / 16 ) - 4

⇒ { a - ( 1/a ) }² = ( 289 - 64 ) / 16

⇒ { a - ( 1/a ) }² = 225/16

⇒ { a - ( 1/a ) } = √( 225 / 16 )

∴  a - ( 1/a ) = ± 15/4




Hope it helps !
Answered by siddhartharao77
9
Given:

= > a + 1/a = 17/4.

On Squaring both sides, we get

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

= > a^2 + 1/a^2 + 2 * a * 1/a = 289/16

= > a^2 + 1/a^2 + 2 = 289/16

= > a^2 + 1/a^2 = 289/16 - 2

= > a^2 + 1/a^2 = 257/16.


We know that (a - 1/a)^2 = a^2 + 1/a^2 - 2 * a * 1/a

                                         = 257/16 - 2 

                                         = 225/16

 = > (a - 1/a) = 15/4.


Hope this helps!
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