Question

If x^2-5x+1=0 then find the value of x^3+1/x^3.

Please send me the answer as soon as possible. Okay?!ASAP!!

Answer 1

Given x^2 - 5x + 1 = 0

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

= > x^2 + 1 = 5x

On dividing both sides by x, we get

$\frac{x^2}{x} + \frac{1}{x} = \frac{5x}{x}$

$x + \frac{1}{x} = 5$

On squaring both sides, we get

$(x + \frac{1}{x} )^2 = (5)^2$

x^2 + 1/x^2 + 2 = 25

x^2 + 1/x^2 = 23.


On cubing both sides, we get

(x + 1/x)^3 = (5)^3

x^3 + 1/x^3 + 3 * x * 1/x(x + 1/x) = 125

x^3 + 1/x^3 + 3(5) = 125

x^3 + 1/x^3 + 15 = 125

x^3 + 1/x^3 = 125 - 15

x^3 + 1/x^3 = 110.


Hope this helps!