Question

If x+1/x =2 and x not equal to zero,find x⁴+1/x⁴​

Answer 1

Question:-

➡ If x + 1/x = 2 and x ≠ 0 then find the value of x⁴ + 1/x⁴

Answer:-

➡ The value if x⁴ + 1/x⁴ is 2.

Solution:-

Given that,

➡ x + 1/x = 2

➡ (x² + 1)/x = 2

➡ x² + 1 = 2x

➡ x² - 2x + 1 = 0

➡ (x - 1)² = 0

➡ (x - 1) = 0

➡ x = 1

Hence, x = 1 is the solution of the equation.

Now,

x⁴ + 1/x⁴

= 1⁴ + 1/1⁴

= 1 + 1

= 2.

Hence,

➡ x⁴ + 1/x⁴ = 2

Also,

xⁿ + 1/xⁿ = 2.

Answer 2

Answer:

( x ² + 1 / x² ) ² - 2 × x² × 1 / x²

( { x - 1 / x }² - 2 × x × 1 / x) ²- 2

( { 2 } ² - 2 ) ² - 2

( 4 - 2 ) ² - 2

( 2 )² - 2

4 - 2

2