I WANT SOLUTION OF THE FOLLOWING QUESTION :-

Q - DIFFERENCE OF TWO PERFECT CUBES IS 189 . IF THE CUBE ROOT OF THE SMALLER OF THE TWO NUMBER IS 3 , FIND THE CUBE ROOT OF THE LARGER NUMBER .

Answer :

Let larger number  =  x 

And

Smaller number  =  y 

So, From first condition , we get

x³ -  y³ =  189

And from second condition , we get

$$\begin{gathered} \sqrt[3 ]{y^3} = 3 \\ \Rightarrow y = 3 \end{gathered}$$

So,

x³  - 3³ = 189

x³  - 27= 189

x³   = 216

So,

Cube root of larger number  = $\sqrt[3 ]{x^3} = \sqrt[3 ]{216} = \sqrt[3 ]{6^3} = \mathbf{6}$                                 ( Ans )