Question

If x+1/x = under root 5, find the value of x^2+1/×^2 and x^4+1/x^4 please answer for solution. ​

Answer 1

Solution :-

x + 1/x = √5

Doing square both side

(x + 1/x)² = (√5)²

x² + 1/x² + 2 = 5

x² + 1/x² = 3

Again doing square both side

(x² + 1/x²)² = (3)²

x⁴ + 1/x⁴ + 2 = 9

x⁴ + 1/x⁴ = 9 - 2

x⁴ + 1/x⁴ = 7

Answer 2

Answer:

x² + 1/x² = 3

x⁴ + 1/x⁴ = 7

Solution:

• Given : x + 1/x = √5
• To find : x² + 1/x² , x⁴ + 1/x⁴ = ?

We have ;

x + 1/x = √5

Now,

Squaring the both sides , we get ;

=> (x + 1/x)² = √5²

=> x² + 2•x•(1/x) + (1/x)² = 5

=> x² + 2 + 1/x² = 5

=> x² + 1/x² = 5 - 2

=> x² + 1/x² = 3

Hence ,

x² + 1/x² = 3

Again ,

Squaring both the sides , we get ;

=> (x² + 1/x²)² = 3²

=> (x²)² + 2•x²•(1/x²) + (1/x²)² = 9

=> x⁴ + 2 + 1/x⁴ = 9

=> x⁴ + 1/x⁴ = 9 - 2

=> x⁴ + 1/x⁴ = 7

Hence ,

x⁴ + 1/x⁴ = 7