Question

is there a number which is equal to its cube but not equal toits square ? if yes find it​

Answer 1

Answer:

-1 is the number,.

Step-by-step explanation:

Given :

To find a number whose cube is equal to it, with it's square unequal to it,.

Solution :

Proof :

Let's say x be a number with that property,.

x = x³ ...(i)

x ≠ x² ...(ii)

x³ ≠ x ...(iii)

By (i),

x = x³

⇒ x = x × x²

⇒ 1 = x²

⇒ ±1 = x i.e., x = 1 (or) x = -1,.

If x = 1,.

⇒ 1 = 1³ ⇒ x = x³ ...(i) is true,.

⇒ 1 = 1² ⇒ x ≠ x² ...(i) is not true,.

So,

x = -1

x = x³

⇒ -1 = (-1)³

⇒ -1 = -1

x ≠ x² & x² ≠ x³

⇒ -1 ≠ (-1)² & (-1)² ≠ (-1)³

⇒ -1 ≠ 1 & 1 ≠ -1 ...(ii) & (iii) are also true,.

∴ -1 is the required number,.

Answer 2

Answer:

-1 is the number

$when \: cubed \\ - 1 \times - 1 \times - 1 = - 1 \\ it \: is \: \: equal \: to \: its \: cube \: \\ when \: squared \\ - 1 \times - 1 = 1 \\ it \: is \: not \: equ \: to \: its \: square$

Hope it is helpful......