is there a number which is equal to its cube but not equal toits square ? if yes find it
Answers
Answered by
3
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,.
Answered by
1
Answer:
-1 is the number
Hope it is helpful......
Similar questions