Question

If x -1/x = 2, then x^4+1/x^4 is equal to​

Answer 1

answer is in the picture

hope it helps

Answer 2

Step-by-step explanation:

Given :-

x-(1/x) = 2

To find :-

Find the value of x⁴+(1/x⁴) ?

Solution :-

Given that

x-(1/x) = 2

On squaring both sides then

=> [ x-(1/x)]² = 2²

=> (x)²-2(x)(1/x)+(1/x)² = 4

Since, (a-b)² = a²-2ab+b²

=> x²-2(x/x) +(1/x²) = 4

=> x²-2(1)+(1/x²) = 4

=> x²-2+(1/x²) = 4

=> x²+(1/x²) = 4+2

=> x²+(1/x²) = 6

Again , on squaring both sides

=> [ x²+(1/x²)]² = 6²

=> (x²)²+2(x²)(1/x²)+(1/x²)² = 36

Since, (a+b)² = a²+2ab+b²

=> x⁴+2(x²/x²) +(1/x⁴) = 36

=> x⁴+2(1)+(1/x⁴) = 36

=> x⁴+2+(1/x⁴) = 36

=> x⁴+(1/x⁴) = 36-2

=> x⁴+(1/x⁴) =34

Answer:-

The value of x⁴+(1/x⁴) is 34

Used Identities :-

→ (a+b)² = a²+2ab+b²

→ (a-b)² = a²-2ab+b²