Question

f x+(1/x) = 3, then, x7 + (1/x7 ) = ?​

Answer 1

Answer:

${x}^{7} + \frac{1}{ {x}^{7} } = 843$

Step-by-step explanation:

Given,

→ $x + \frac{1}{x} = 3$ - eq.1

Squaring on both sides:

→ ${x}^{2} + \frac{1}{ {x}^{2} } + 2 = 9$

→ ${x}^{2} + \frac{1}{ {x}^{2} } = 7$ - eq.2

Squaring on both sides:

→ ${x}^{4} + \frac{1}{ {x}^{4} } + 2 = 49$

→ ${x}^{4} + \frac{1}{ {x}^{4} } = 47$ - eq.3

Multiply eq.1 and eq.2:

→ $(x + \frac{1}{x} )( {x}^{2} + \frac{1}{ {x}^{2} } ) = 7 \times 3$

→ $( {x}^{3} + \frac{1}{ {x}^{3} } ) + (x + \frac{1}{x} ) = 21$ - eq.4

Substitute eq.1 in eq.4:

→ ${x}^{3} + \frac{1}{ {x}^{3} } = 18$ - eq.5

Multiply eq.3 and eq.5:

→ $( {x}^{4} + \frac{1}{ {x}^{4} } )( {x}^{3} + \frac{1}{ {x}^{3} } ) = 18 \times 47$

→ $( {x}^{7} + \frac{1}{ {x}^{7} }) + (x + \frac{1}{x} ) = 846$ - eq.6

Substitute eq.1 in eq.6:

→ ${x}^{7} + \frac{1}{ {x}^{7} } = 843$

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