Question

x+1/x=7,thenx^2+1/x^2=?​

Answer 1

Answer:

x²+1/x² = 51

Step-by-step 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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Answer 2

Given: x + 1/x = 7

Squaring on both sides

⇒ (x + 1/x )² =(7)²

⇒ x² + ( 1/x)² + 2(x)(1/x) = 49

[∵ (a+b)²=a²+b² + 2ab]

⇒ x² + 1/(x²) + 2 = 49

⇒ x² + 1/(x2) = 49 - 2

∴ x² + 1/(x²) = 47

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