(solved)Question 7 SSC-CGL 2020 March 3 Shift 1

Question 7
SSC-CGL 2020 Mar 3 Shift 1

If x - y = 4, and xy = 45, what is the value of (x³ - y‎³)?

Solution in Brief

By shear guess x = 9, y = 5 satisfy both the given conditions, so x³ - y‎³ = 9³ - 5³ = 604 answer!

Solution by Longer Method

By the standard algebraic identity,

$\displaystyle (x - y)^3 = x^3 - y^3 - 3xy(x- y)$

which can be re-arranged to get

$ \begin{aligned} x^3 - y^3 &= (x - y)^3 + 3xy(x - y)\\ &=4^3 + 3\cdot 45 \cdot 4\\ &= 604\:\underline{Ans} \end{aligned} $