Question

if x²+1/x²=98,then find the value of [x³+1/x³]​

Answer 1

Answer :

x³ + 1/x³ = 970

Solution :

• Given : x² + 1/x² = 98
• To find : x³ + 1/x³ = ?

We know that ,

(A + B)² = A² + B² + 2AB

If A = x and B = 1/x , then

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

=> (x + 1/x)² = x² + 1/x² + 2

=> (x + 1/x)² = 98 + 2

=> (x + 1/x)² = 100

=> x + 1/x = √100

=> x + 1/x = 10

Now ,

Cubing both the sides , we get ;

=> (x + 1/x)³ = 10³

=> x³ + (1/x)³ + 3•x•(1/x)•(x + 1/x) = 1000

=> x³ + 1/x³ + 3•1•10 = 1000

=> x³ + 1/x³ + 30 = 1000

=> x³ + 1/x³ = 1000 - 30

=> x³ + 1/x³ = 970

Hence ,

x³ + 1/x³ = 970