If x + 1/x = −2√3, what is the value of x⁵ + 1/x⁵?

Let s = x+1/x = −2√3. Then x²+1/x² = s²−2 = 12−2=10. x³+1/x³ = s³−3s = −24√3+6√3 = −18√3. x⁵+1/x⁵ = (x²+1/x²)(x³+1/x³)−(x+1/x) = 10×(−18√3)−(−2√3) = −180√3+2√3 = −178√3. Answer is (a) −178√3.