1.

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

Answer»

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.


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