If 2x²- 7x + 5 = 0, then what is the value of x³+ 125/(8x³)?

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

Show answer & explanation

Correct answer: C

Explanation

The correct answer is Option 3 i.e $16\frac{5}{8}$ .

2x²- 7x + 5 = 0

⇒ x(2x - 7 + 5/x) = 0

⇒ 2x + 5/x = 7

Cubing both sides

8x³ + (125/x³) + 3 × 2x × 5/x (2x + 5/x) = 343

⇒ 8x³ + (125/x³) = 343 - 210

⇒ 8x³ + (125/x³) = 133

Dividing by 8 on both sides

(x³ + 125/8x³) = 133/8 = $16\frac{5}{8}$

SSC CGL 2021 PYQ — Question 54