Square or double, fair or trouble

Algebra Level 1

When first introduced to exponents, many students think that

$n ^2 = 2 n.$

Find the positive integer $n$ for which the equation is true.

The answer is 2.

10 solutions

Soham Dibyachintan
Nov 19, 2013

Given the equation, $n^{2}=2 \times n$ $\Rightarrow n=\frac{2 \times n}{n}$ $\Rightarrow n=2$ Thus, $\boxed{n=2}$

If a student is an idiot than yes indeed.

aaryan vaishya - 2 years, 3 months ago

Sarang Deshmukh
Nov 18, 2013

nn=2 n

take n=2

4=4 so ans is 2

simple method ,,i liked

faisal mehmood - 7 years, 6 months ago

or you could divide both sides by n and you still left with n=2

rasin gani - 7 years, 6 months ago

Budi Kurniawan
Nov 17, 2013

n^2 = 2n => n^2 - 2n = 0 => n(n-2) = 0 = > n = 0 V n-2 = 0; n = 2, 2 is possible answer

Kou$htav Chakrabarty
Nov 19, 2013

1st Solution: Given expression: $n^2=2n$ $or, n \times n=2n$ Cancelling n on both sides, we get: $or, \boxed{n=2}$
2nd Solution It is given that n is a positive integer. So, possible values of * n = 1, 2, 3, 4, .... * If we look closely, the expression asks us to find a natural number whose square is the same as its product with 2. And, there is only one natural number whose square is the same as its product with 2 and that is 2 .

*PLZ. NOTE : The second solution is deprecated and inappropriate for solving these kind of problems(because as equations keep getting bigger, it gets more complex). Since, n^2 = 2n is quite special as it tells a unique property of 2, I thought I'd post it for the benifit of the younger members of this BRILLIANT website!!! ;) *

Ronald Cadavillo
Jan 4, 2014

Marc Tugadi
Nov 19, 2013

2^2=2(2) 4=4

Hellooooo Friends
Nov 18, 2013

n^2 = 2n <=> n . n = 2 . n <=> n = 2

Is $n=2$ the only solution to your equation?

Calvin Lin Staff - 7 years, 6 months ago

Really, this is equation is same : $n^2 - 2n$ = $0$ , where I passed the $2n$ to the first member, so using Girard we have. $\rightarrow$ sum = $\frac{-b}{a}$ = $\frac{2}{1}$ ; $\rightarrow$ product = $\frac{c}{a}$ = $0$ , so the roots are $\boxed{2}$ and $\boxed{0}$

Ewerton Cassiano - 7 years, 6 months ago

Sakshi Jain
Nov 18, 2013

n square = 2 square = 4

and 2n=2*2 = 4

It's better if you use LaTex Code next time, as it makes the solution more elegant and pleasant to look at. :)

Akshat Jain - 7 years, 6 months ago

Yup! I agree(I love using LateX and read over my answers again and again after using it !!!!).

Kou$htav Chakrabarty - 7 years, 6 months ago

Vishnu Rajeev
Nov 18, 2013

n^2=2n

then,

n=2

2^2=2*2

4=4.

Sin Joey
Nov 17, 2013

2X2=4

2(2)=4