Question

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★ Check if there is any Number which If cubed, gives the Number itself.
But, if squared, does not gives the number itself.

➳ REQUIRED GOOD ANSWER
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Answer 1

Answer:

The number is -1

Proof :-

(-1)² = 1

(-1)³ = -1

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Answer 2

Question:

To find a number which If cubed, gives the Number itself.

But, if squared, does not gives the number itself.

Given:

A number when cubed gives the number itself but when squared does not gives the number itself.

To Find:

The number when cubed gives the number itself but when squared does not gives the number itself.

Solution:

Let the number be x

x³ = x

x² ≠ x

So lets consider the number x = 1

Conditions:

1. x³ = x
2. x² ≠ x

• 1³ = 1

• Whereas 1² = 1

• The condition denies so the x ≠ 1

• Since the square of 1 is equal to itself so it denies.

So lets consider the number x = 2

Conditions:

1. x³ = x
2. x² ≠ x

• 2³ = 8

• Whereas 2² = 4

• The condition denies so the x ≠ 2

• Since the cube of 2 is  not equal to itself so it denies.

So we cant consider any number greater then 2 because the cube and the square will be greater than itself.

So lets consider the number x = 0

Conditions:

1. x³ = x
2. x² ≠ x

• 0³ = 0

• Whereas 0² = 0

• The condition denies so the x ≠ 0

• Since the square of 0 is   equal to itself so it denies.

So lets consider the number x = -1

Conditions:

1. x³ = x
2. x² ≠ x

• -1³ =  -1

• Whereas -1² = 1

• The condition satisfies so the x = 0

• Since the square of -1 is  not  equal to itself and the cube of -1 is equal to itself so it satisfies.

The required number is -1

Answer:

x = -1