Question

if x - 1/x = 3/2, find the value of x+1/x​

Answer 1

Step-by-step explanation:

(x+ x1 ) 2 =x 2 + x 2 1 +2×x× x1

⇒(3) 2 =x 2 + x 2 1 +2

⇒9=x 2 + x 2 1 +2⇒

x 2 + x 2 1 +2=9

⇒x 2 + x 2 1 =9−2=7

∴x 2 + x 2 1 =7

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Answer 2

Step-by-step explanation:

A good approach to this problem would be by using the fact that (a−b)2=(a+b)2−4ab(a−b)2=(a+b)2−4ab

The main reason behind using this is the fact that the 4ab4ab term in this case simplifies as 4∗x∗1x=44∗x∗1x=4

Proceeding with the first formula and substituting a=xa=x and b=1xb=1x, we have:

(x−1x)2=(x+1x)2−4∗x∗1x(x−1x)2=(x+1x)2−4∗x∗1x

⟹(x−1x)2=(x+1x)2−4⟹(x−1x)2=(x+1x)2−4

Substituting the value of x+1xx+1x as given in the question, we have

(x−1x)2=92−4(x−1x)2=92−4

⟹(x−1x)2=77⟹(x−1x)2=77

⟹x−1x

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