Question

Difference of two perfect cubes is 189. If the cube root of the smaller of the two numbers is 3, find the

cube root of the larger number.

Answer 1

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Let the two nos be x and y

Now given -: Difference of two numbers which are perfect cubes is 189

⇒x^3 - y^3 = 189

Let y be the smaller of the two nos

and the cube root of the smaller [y] of the two numbers is 3

⇒ y=3

find the cube of 3 and that is 27

⇒ y^3  = 27

ATP

⇒ x^3 - y^3 = 189

=> x^3 -27 =189  [Putting the value of y^3  = 27]

=> x^3 =189 +27

=> x^3= 216

Cube root of (216) = 6

⇒ x=6

Therefore, the larger number is 6. Ans

and the smaller number is 3   .

Answer 2

hope it helps you !................