Question

If x + 1 x =3 find the value of x2 + 1 x 2 and x4 + 1 x 4

Answer 1

Answer:

7,47

Step-by-step explanation:

x+1/x = 3

(x+1/x)² = 3² [ Squaring both the sides ]

x²+1/x²+2×x×1/x = 9

x²+1/x²+2 = 9

x²+1/x² = 7

(x²+1/x²)² = (7)² [Squaring both the sides]

x⁴+1/x⁴+2×x²×1/x² = 49

x⁴+1/x⁴+2 = 49

x⁴+1/x⁴ = 47

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Answer 2

$x + \frac{1}{x} = 3 \\ ( {x + \frac{1}{x} })^{2} = 9 \\ {x}^{2} + \frac{1}{ {x}^{2} } + 2 = 9 \\ {x}^{2} + \frac{1}{ {x}^{2} } = 7 \\ ( { {x}^{2} + \frac{1}{ {x}^{2} } })^{2} = 49 \\ {x}^{4} + \frac{1}{ {x}^{4} } + 2 = 49 \\ {x}^{4} + \frac{1}{ {x}^{4} } = 47$