Question

x+1/x=7, find xsquare-1/xsquare​

Answer 1

Answer:

x-1/x=7

Squaring both sides,

(x-1/x)²=7²

(x)²+(1/x)²-2×x×1/x=49

x²+1/x²-2=49

x²+1/x²=49+2

x²+1/x²=51

Answer 2

Answer:

x²+1/x² = 51

Explanation:

Given x - 1/x = 7 ---(1)

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We know the algebraic identity:

a²+b²-2ab = (a-b)²

Or

a²+b² = (a-b)²+2ab

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Now,

x²+1/x²

= (x-1/x)²+2*x*(1/x)

= (x-1/x)²+2

= 7²+2 [ from (1)]

= 49+2

= 51

Therefore,

x²+1/x² = 51

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