Question

If x²+1/x²=7 find the value of x³+1/x3

Answer 1

Answer:

±18

(Both are possible; however if you also know that x is positive, then 18 must be the answer.)

Step-by-step explanation:

First...

(x + 1/x)²  =  (x² + 1/x²) + 2  =  7 + 2  =  9

⇒  x + 1/x  =  ±3

Then...

(x + 1/x)³  =  x³ + 3x + 3/x + 1/x³

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

                   =  (x + 1/x) [ (x + 1/x)² - 3 ]

                   =  ±3 × (9 - 3)

                   =  ±3 × 6

                   =  ±18