If x = 2+√3, find the value of x +1/x.
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Answered by
0
Answer:4
Step-by-step explanation:
X=2+√3
Therefore
1/X=1/2+√3
=(1/2+√3)*(2-√3/2-√3)
=2-√3
Hence
X+1/X=2+√3+2-√3=4
Answered by
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Given : x = 2 + √3 . …..(1)
or 1/x = 1/(2 + √3)
By Rationalizing denominator, we have :
= 1 × (2 - √3) / [(2 + √3) × (2 - √3)]
= (2 - √3) / (2)² - (√3)²
[We know that, (a + b) (a - b) = a² - b²]
= (2 - √3)/(4 - 3)
= (2 - √3 )/1
= 2 - √3
1/x = 2 - √3 ………(2)
Then, x + 1/x
On putting the value from eq 1 & 2 :
= (2 + √3) + (2 - √3)
= 2 + 2
= 4
Hence, the value of x +1/x is 4.
HOPE THIS ANSWER WILL HELP YOU…..
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