If x² + 1/x² = 7 and x is positive, then x³ + 1/x³ equals:

Question

Accepted Answer

18. Since (x + 1/x)² = x² + 1/x² + 2 = 9 and x is positive, x + 1/x = 3. Then x³ + 1/x³ = (x + 1/x)³ − 3(x + 1/x) = 27 − 9 = 18. (27 stops at the cube, 24 subtracts (x + 1/x) instead of 3(x + 1/x), and 21 is just 3 × 7.)

If $x^{2} + 1/ x^{2} = 7$ and $x$ is positive, then $x^{3} + 1/ x^{3}$ equals:

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If x2+1/x2=7 and x is positive, then x3+1/x3 equals:

Step-by-Step Solution

Master this topic in 30 minutes a day.

More Algebra practice

If $x^{2} + 1/ x^{2} = 7$ and $x$ is positive, then $x^{3} + 1/ x^{3}$ equals: