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

$\bf{\huge{\underline{\boxed{\rm{\red{Answer:}}}}}}$

Given:-

• Difference of two perfect cubes is 189
• The cube root of the smaller of the two numbers is 3

To find :-

• The cube root of the larger number

Solution :-

Let the larger number be x and smaller number be y.

As per the first condition,

• Difference of two perfect cubes is 189

x³ - y³ = 189 ----->1

As per the second condition,

• Cube root of the smaller number is 3

Smaller number = y = 3

Find the cube of the smaller number, y = 3³ = 3 × 3 × 3 = 27

Value of the cube of the smaller number, y = 27

Substitute the value of y in equation 1 to find the cube root of the larger number.

x³ - y³ = 189

x³ - 27 = 189

x³ = 189 + 27

x³ = 216

x = √216

x = 6

•°• Cube root of larger number, x = 6

$\bf{\huge{\underline{\boxed{\tt{\blue{Verification:}}}}}}$

As per the question,

• difference of two perfect cubes is 189

Cube of smaller number, y = 27

Cube of larger number, x = 216

Difference = 189

x³ - y³ = 189

216 - 27 = 189

189 = 189

LHS = RHS.

Answer 2

$\bold {\huge {Answer :-}}$

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➛Let larger number = x

➛Smaller number = y

From first condition ✭

Difference of two numbers which are perfect cubes is 189 

⇒x³ - y³ = 189

⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯

And from second condition ✭

we get

$\Rightarrow \:\:^3\sqrt{y^3}= 3$

⇒y =3

So

⇒x³ - 3³ = 189

⇒x³ - 27= 189

⇒ x³ = 216

Hence, Cube root of larger number

$\Large\bold{\Rightarrow^3\sqrt{x^3}=^3\sqrt{216}=^3\sqrt{6^3} =6}$