Question

If X+1/x=5 find the value of x2+1/x2​

Answer 1

☆$\small\green {\sf{Answer }}$☆

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(x + 1 /x ) = 5

We need to find X2+ 1 / x2

( x + 1 / x )2 = 25

= x2 + 1 / x2 + 2 (x)(1)(1/x) =25

= x2 + 1/x2 + 2 = 25

= X2 + 1 / x2 = 25 – 2

= X2+ 1 / x2=23

X2+ 1 / x2= 23

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Answer 2

Step-by-step explanation:

x2−(1x)2=(x+1x)(x−1x)x2−(1x)2=(x+1x)(x−1x)

We know that (a+b)2=(a−b)2+4ab(a+b)2=(a−b)2+4ab

Hence, (x+1x)2=(x−1x)2+4⋅x⋅1x=25+4=29(x+1x)2=(x−1x)2+4⋅x⋅1x=25+4=29

Hence the required solution is ±529−−√