Question

if x = 5+√24 then find the value of (x + 1/x)^2.​

Answer 1

Step-by-step explanation:

here is your answer and once try to solve it yourself

Answer 2

Step-by-step explanation:

We have been given ,

x = 5 + √24 ..............(1)

So , we can write

1/ x = 1 / ( 5 + √24 )

[ Rationalising the denominator , we get ]

For , rationalising we have to multiply the denominator and numerator with 5 - √24 .

So ,

1/ x = ( 5 - √24 ) / ( 5 + √24 ) ( 5 - √24 )

→ 1/x = ( 5 - √24 ) / ( 5^2 - 24 )

[ Since , a^2 - b^2 = ( a + b ) ( a - b ) ]

→ 1/x = (5 - √24 ) / ( 25 - 24 )

→ 1/x = ( 5 - √24 ) / 1 = 5 - √24 ............(2)

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Final process

( x + 1/x ) ^2 = ( 5 + √24 + 5 - √24 ) ^2

{ Using equation (1) and (2) }

→ ( x + 1/x ) ^2 = (10)^2 = 100

Hence, the required answer is 100.

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