Question

if X+1/X=3 then calculate the value of
${x5 + 1 \div x5}^{?}$

Answer 1

x+1/x=3--->x+1=3x
             ---->2x=1
             ---->x=1/2

x^5+1/x^5 = 33

Answer 2

Answer:

x^5 + 1/x^5 = 123

Step-by-step explanation:

Given x+1/x=3 = k

x- 1/x = √k² - 4 = √9 - 4 = √5..............i

x^5 + 1/x^5 = ?

x² + 1/x² = k² - 2 = 3² - 2 = 7

x³ + 1/x³ = k³ - 3 k = 3³ - 3 (3) = 27 - 9 = 18 = p

x³ - 1/x³ = √p²-4 = √18²- 4 = √324 - 4 = √320

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

= x^5 - 1/x^5 + x - 1/x

= x^5 - 1/x^5 + √5

means

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

= 7 * √320 - √5

7 * √2 * 16 * 2 * 5 - √5

= 7 * 4 * 2 √5 - √5

= 56√5 - √5 = 55√5 = n

Now,

x^5 + 1/x^5 = √n² + 4 = √(55√5)² + 4 = √15125 + 4 = √15129 = 123

x^5 + 1/x^5 = 123