Math, asked by nishantinferno, 1 year ago

If x=9+4 root 5 then find root x-1/root x

Answers

Answered by mysticd

Solution :

x = 9 + 4√5

= 9 + 2√4×5

= 5 + 4 + 2•√4•√5

= (√5)²+(√4)²+2•√4•√5

= (√5 + √4 )²

= (√5 + 2 )²

i ) √x = √(√5 + 2)²

= √5 + 2 ----( 1 )

ii ) 1/√x = 1/(√5 + 2 )

= (√5 -2 )/[(√5+2)(√5-2)]

= (√5-2)/( 5 - 4 )

= √5 - 2 ---( 2 )

Now ,

√x - 1/√x

= √5 + 2 - ( √5 - 2 )

= √5 + 2 - √5 + 2

= 4

Or

2√5

••••

nishantinferno: It's root x-1/root x

Anonymous: No worries. Call the correct answer y, so y = root x - 1/root x. Then y^2 = x + 1/x + 2. Changing the sign in the last step of the solution above (or below!), you get x + 1/x = 18. So y^2 = 20. So y = 2root5. (we can rule out the negative option because x > 1, so 1/x < x which means that y is positive)

Anonymous: Oops, sign problems again. I meant y^2 = x + 1/x - 2 = 18 - 2 = 16. So y = 4.

Anonymous: If this helps, plzzz mark solution below brainliest!

Answered by Anonymous

Answer:

Step-by-step explanation:

1 / x = 1 / ( 9 + 4√5 )

= ( 9 - 4√5 ) / ( 9² - (4√5)² ) (multiplied numerator and denominator by conjugate)

= ( 9 - 4√5 ) / ( 81 - 80 )

= 9 - 4√5

So x - 1 / x = ( 9 + 4√5 ) - ( 9 - 4√5 ) = 8√5

nishantinferno: Wrong answer!, WELCOME TO KAUN BANEGA CROREPATI THE ANSWER IS 4

Anonymous: Yes, that matter has already been discussed and resolved in the comments above!

Anonymous: By myself no less!!!

Anonymous: Nonetheless.... glad my solution + corrections helped you!

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