Question 65

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

Solution

$$2x^2-7x+5=0$$

$$2x^2-2x-5x+5=0$$

$$2x\left(x-1\right)-5\left(x-1\right)=0$$

$$\left(x-1\right)\left(2x-5\right)=0$$

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

$$x=1$$ or $$x=\frac{5}{2}$$

When $$x=1$$,

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

Hence, the correct answer is Option B

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