Question

If x2 -5x+1 = 0 , then x3 + 1/x3 is equal to ???

Answer 1

Answer:

110

Step-by-step explanation:

Given:

x² - 5x + 1 = 0

To find:

The value of

${x}^{3} + \dfrac{1}{ {x}^{3} }$

Solution:

${x}^{2} - 5x + 1 = 0 \\ \\ {x}^{2} + 1 = 5x$

[Dividing both side by x ]

$x + \dfrac{1}{x} = \: 5 \: \: ---(1)$

[Now, cubing both side ]

${(x + \frac{1}{x} )}^{3} = {5}^{3} \\ \\ {x}^{3} + \frac{1}{ {x}^{3} } + 3.x. \frac{1}{x}( x + \frac{1}{x} ) = 125 \\ \\ {x}^{3} + \frac{1}{ {x}^{3} } + 3. \cancel{x}. \frac{1}{\cancel{x}} ( x + \frac{1}{x} ) = 125$ ${x}^{3} + \frac{1}{ {x}^{3} } + 3(5) = 125 \:\:\: [\text{From 1}] \\ \\ {x}^{3} + \frac{1}{ {x}^{3} } = 125 - 15 \\ \\ {x}^{3} + \frac{1}{ {x}^{3} } = 110$

Therefore, the required answer is 110.

Formula Used

See in the attachment.

Answer 2

Answer:

110

Step-by-step explanation:

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