Question

if x+1/x=3 find the value of x6+1/x6

Answer 1

Answer :- 322

Explanation :-

x + 1/x = 3 ....... (given)......... (equation-1)

So x^6 + 1/x^6 =????

Squaring both sides in equation 1, we get

=> (x + 1/x)² = 3²

=> x² + 1/x² + (2*x*1/x) =9

=> x² + 1/x² + 2 = 9

=> x² + 1/x² = 7.......(equation-2)

Now cubing both sides in (equation-2), we get

=> (x² + 1/x²)³ = 7³

=> (x²)³ + (1/x²)³ + 3*x²*1/x²(x² + 1/x²) = 343

=> x^6 + 1/x^6 + 3(7) = 343.... (From equation-2)

=> x^6 + 1/x^6 = 343 - 21

=> x^6 + 1/x^6 = 322....(Answer)

Hope it will help you.....