If x= 4-√5 then value of x+ 1/x is equal to
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Answer:
Step-by-step explanation:
At first Rationalize x
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Answer:
x + 1/x = (48 - 10√5) / 11
Solution:
Given : x = 4 - √5
To find : x + 1/x = ?
We have ,
x = 4 - √5
Thus,
1/x = 1/(4 - √5)
Now,
Rationalising the denominator of the term in RHS , we have ;
=> 1/x = (4 + √5)/(4 - √5)(4 + √5)
=> 1/x = (4 + √5)/[ 4² - (√5)² ]
=> 1/x = (4 + √5) / (16 - 5)
=> 1/x = (4 + √5)/11
Thus,
x + 1/x = (4 - √5) + (4 + √5) / 11
= [ 11(4 - √5) + (4 + √5) ] / 11
= ( 44 - 11√5 + 4 + √5 ) / 11
= (48 - 10√5) / 11
Hence,
x + 1/x = (48 - 10√5) / 11
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