Question

if x2+1/x2 = 18 then find value of x3- 1/x3 ?

Answer 1

x² + 1/x² = 14

(x + 1/x)² -2.x.1/x = 14

(x + 1/x )² -2 = 14

(x + 1/x )² = 16

take square root both sides

(x + 1/x) = 4

then,

x³ + 1/x³ = ( x + 1/x)³ - 3.x.1/x(x + 1/x)

= ( x +1/x)³ -3(x + 1/x)

= (4)³ -3(4)

= 64 - 12

= 52

Answer 2

in easy frist find value of x in frist expression x2+1/x2=18
frist cross multiplication
=x2+1=18×x2
=x2+1=36x
=x2-36x=-1
=-34x=-1
=x=-1/-34
so value in second xpression
1/34×3-1/1/34×3
=and that is zero