Question

if x+1/x=5 then x^5+1/x^5=?
​

Answer 1

Answer:

Step-by-step explanation:

x+1/x = 5

x²+1/x²+2=25

x²+1/x²=23

(x+1/x)³=125

x³+1/x³+3(x+1/x)=125

x³+1/x³+3(5)=125

x³+1/x³=125-15 = 110

(x^5+1/x^5) = (x³+1/x³)(x²+1/x²)-(x+1/x)

(x^5+1/x^5) = (110)(23)-5

(x^5+1/x^5) = 2530-5

x^5+1/x^5 = 2525

if you like answer please mark me as brainliest answer.

Answer 2

★some important thought:-

$\implies \: (x {}^{2} + \frac{1}{x {}^{2} } )(x {}^{3} + \frac{1}{x {}^{3} } ) = x {}^{5} + \frac{1}{x {}^{5} } + x + \frac{1}{x} - - (1)$

$\implies \: x + \frac{1}{x {}^{} } = 5 \\ \\ \implies \: x {}^{2} + \frac{1}{x {}^{2} } = 5 {}^{2} - 2 \\ \\ \implies \: x {}^{2} + \frac{1}{x {}^{2} } = 23 - - (2)$

$\implies \: x {}^{3} + \frac{1}{x {}^{3} } = 5 {}^{3} - 3(5) \\ \\ \implies \: x {}^{3} + \frac{1}{ {x}^{3} } = 110 - - (3)$

we find answer eq 1 , 2 and 3

$\implies \: 23 \times 110 = x {}^{5} + \frac{1}{x {}^{5} } + 5 \\ \\ \implies \: x {}^{5} + \frac{1}{x {}^{5} } = 2530 - 5 = 2525$

__________________________

thanks