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Question:

If 2x²  - 7x + 5 = 0, then what is the value of x³ + $\frac{125}{8x^3}$?

Explanation:

2x² - 7x + 5 = 0

2x² - 2x - 5x + 5 = 0

2x(x - 1) - 5(x - 1) = 0

(x - 1) (2x - 5) = 0

x - 1 = 0 or 2x - 5 = 0

x = 1 or x = $\frac{5}{2}$

When x = 1,

x³ + $\frac{125}{8x^3}$ = (1)³ + $\frac{125}{8{\left(1\right)}^3}$ = 1 + $\frac{125}{8}$ = $\frac{133}{8}$ = 16$\frac{5}{8}$

Hence, the correct answer is Option B