If x2 + (1/x2) = 31/9 and x > 0, then what is the value of x3 + (1/x3) ?

Correct Answer: 666

Correct Answer: 20

Correct Answer: 2

Correct Answer: 2?3

Correct Answer: ± ?21

Correct Answer: 4/3

Correct Answer: 1

Correct Answer: 1

Correct Answer: cos2A

Correct Answer: Each fraction is equal to 1/2 or -1

Explanation:

a/(b+c) = b/(c+a) = c/(a+b)

Taking reciprocal and adding 1 to each ratio we get;

(b+c)/a + 1 = b/(c+a) + 1 = c/(a+b) + 1

Or (a+b+c)/a = (a+b+c)/b = (a+b+c)/c

So this can only be equal when a=b=c or a+b+c = 0

When a=b=c we get

a/(b+c)= ½When a+b+c = 0 we get

b+c = -a

So a/(b+c) = -1

So the ratios are ½ or -1