SSC CHSL 2021 PYQ — Question 74

The correct answer is option 3 i.e.  $\frac{217}{64}$

Given:

  x - y = 7/4 

$\frac{1}{x}-\frac{1}{y}=\frac{14}{3}$

Concept USed:

(x - y)³ = x³  - y³ - 3(xy)(x - y)

Explanation:

According o the given question,

 ${( y - x) \over xy}=\frac{14}{3}$

⇒${-{7 \over 4} \over xy} = {14 \over 3}$ 

⇒ xy = $-{3 \over 8}$

Now, (x - y)³ = x³  - y³ - 3(xy)(x - y)

⇒ $({7 \over 4})^3 = x^3 - y^3 - 3(-{3 \over 8})({7 \over 4})$

⇒ ${343 \over 64} = x^3 - y^3 + ({63 \over 32})$

⇒${343 \over 64} - {63 \over 32} = x^3 - y^3$

⇒ $x^3 - y^3 = {217 \over 64}$

Hence the required answer is $\frac{217}{64}$.