Question

Please answer it plz plz plz and telle the whole explanation it's right answer is 17/3 and I want solution. ​

Answer 1

Answer:

So the answer is 17/3

Answer 2

Step-by-step explanation:

Given:-

x-(1/x) = 2

To find :-

Find the value of [x⁴+(1/x⁴)] ÷ [ x²+(1/x²)] ?

Solution :-

Given that

x-(1/x) = 2 -----------(1)

On squaring both sides then

[x-(1/x)]² = 2²

=>x²-2(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 --------(2)

On squaring both sides again

[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 ------(3)

On dividing (3) by (2) then

=> [x⁴+(1/x⁴)] ÷ [ x²+(1/x²)]

=> [x⁴+(1/x⁴)] / [ x²+(1/x²)]

=> 34/6

=> 17/3

Answer:-

The value of [x⁴+(1/x⁴)] ÷ [ x²+(1/x²)] is 17/3

Used formulae :-

→ (a+b)² = a²+2ab+b²

→ (a-b)² = a²-2ab+b²

→ (a^m)^n = a^(mn)