You have a number

Algebra Level 2

I have a number.

  • If I multiply it by itself, then it will become larger than before.
  • If I multiply this new number by the original number one more time, then it will become the original number itself.

What is the original number that I started with?


The answer is -1.

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Agnishom Chattopadhyay by Agnishom Chattopadhyay , 22, India

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1 solution

Viki Zeta
Oct 17, 2016

Given; a 2 > a ; and; a 2 × a = a a 3 = a a 3 − a = 0 a ( a 2 − 1 ) = 0 a ( a + 1 ) ( a − 1 ) = 0 a = 0 , a = − 1 , a = 1 a 2 > a ⟹ 0 2 ≯ 0 , 1 2 ≯ , ( − 1 ) 2 > − 1 ∴ a = − 1 \text{Given; }\\ a^2 > a \text{; and; } \\ a^2 \times a = a \\ a^3 = a \\ a^3 - a = 0 \\ a(a^2 - 1) = 0 \\ a(a+1)(a-1) = 0 \\ a = 0, a = -1, a = 1 \\ a^2 > a \\ \implies 0^2 \ngtr 0, 1^2 \ngtr , (-1)^2 > -1 \\ \boxed{\therefore a = -1}

5 Helpful 0 Interesting 0 Brilliant 0 Confused

Well, it is better to explain your steps here. For example, you could say:

Let's call this number a a . Then from the first paragraph, we know that a 2 > a a^2 > a .

And from the second paragraph, we know that a 2 ⋅ a = a 3 a^2 \cdot a = a^3 is equal to a a itself again.

Solving for a 3 = a a^3 = a gives a = 0 , 1 , − 1 a = 0,1, -1 . But since we know that a 2 > a a^2 > a , then a = − 1 a = -1 only.

Agnishom Chattopadhyay - 4 years, 7 months ago

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