Question

if x^2+1/x^2=34 then find the value of x^3+1/x^3 please tell fast​

Answer 1

Answer :

x³ + 1/x³ = 198

Solution :

• Given : x² + 1/x² = 34
• To find : x³ + 1/x³ = ?

We know that ,

(A + B)² = A² + B² + 2AB

Thus ,

=> (x + 1/x)² = x² + (1/x)² + 2•x•(1/x)

=> (x + 1/x)² = x² + 1/x² + 2

=> (x + 1/x)² = 34 + 2

=> (x + 1/x)² = 36

=> x + 1/x = √36

=> x + 1/x = 6

Now ,

Cubing both the sides , we get ;

=> (x + 1/x)³ = 6³

=> x³ + (1/x)³ + 3•x•(1/x)•(x + 1/x) = 216

=> x³ + 1/x³ + 3•1•6 = 216

=> x³ + 1/x³ + 18 = 216

=> x³ + 1/x³ = 216 - 18

=> x³ + 1/x³ = 198

Hence ,

x³ + 1/x³ = 198