Question

If x2 - 5x + 1 = 0 (X is not equal to 0), then the value of x3 +1/x3
(1) 125
(3) 150
(2) 110
(4) 140
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Answer 1

Answer:

Step-by-step explanation:

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Answer 2

Answer:

$x^3 + \frac{1}{x^3} = 110$

Step-by-step explanation:

Given:

x² - 5x + 1 = 0

To find:

x³ + 1/x³

---------------------------

$x^2 - 5x + 1 =0$

Dividing by x,

$\frac{x^2}{x} + \frac{1}{x} = \frac{5x}{x} \\\\x + \frac{1}{x} = 5\\\\(x + \frac{1}{x})^3 = 5^3\\\\x^3 + \frac{1}{x^3} + 3(x)(\frac{1}{x} )[x +\frac{1}{x}] = 5^3\\\\x^3 + \frac{1}{x^3} + 3[5] = 5^3\\\\x^3 + \frac{1}{x^3} + 15 = 125\\\\x^3 + \frac{1}{x^3} = 125 -15\\\\x^3 + \frac{1}{x^3} = 110$