Question

if x + 1/x = 3 find x^5 + 1/x^5 and x^5 - 1/x^5

Answer 1

Hii friend,

X+1/X = 3

X+1 = 3X

3X-X= 1

2X = 1

X = 1/2

Putting the value of X in,

X^5+1/X^5 = (1/2)^5 + 1/ (1/2)^5

= 1/32+ 1 / 1 / 32

= 1+32/32 / 1/32

= 33 Ans.

Answer 2

HERE'S YOUR ANSWER, FRIEND.
from given equation 1,
${x}^{2} + 1 = 3x \\ {x}^{2} - 3x + 1 = 0 \\ x = \frac{ 3 \pm \sqrt{9 - 4} }{2} \\x = \frac{ 3 \pm \sqrt{5} }{2} \: \: ...............(i)$
so, from equation (i),
when, x = [3 + √(5)]/2,
$\: \: \: \: \: {x}^{5} + \frac{1}{ {x}^{5} } \\ = \frac{{x}^{10} + 1}{{x}^{10}} \\ = \frac{ ({\frac{ 3 + \sqrt{5} }{2})}^{10} + 1 }{ ({\frac{ 3 + \sqrt{5} }{2})}^{10} } \\ = \frac{15126.99 + 1}{15126.99} \\ \approx \: 1.00006$
Similarly, you can find values of other expressions also.