☝️=✌️

Algebra Level 1

$\begin{aligned} 23^2=&23 \cdot 23 \quad & \ldots ① \\ 23^2-23^2=&23 \cdot 23-23 \cdot 23 \quad & \ldots ② \\ (23+23)(23-23)=& 23(23-23) \quad & \ldots ③ \\ (23+23)\cdot \cancel{0}=&23\cdot \cancel{0} \quad & \ldots ④ \\ 23=&46 ⇒ 1=2 \quad & \ldots ⑤\end{aligned}$

The above equations lead us to a conclusion that $1 = 2$ . Then which of these steps contains the flaw.

Try more problems here .

The answer is 4.

2 solutions

Satyabrata Dash
May 30, 2016

According to properties of real numbers if a , b , c are real numbers , then,

$\Large ab=ac → b=c$

is justified only when $a\neq 0$ since to obtain $b=c$ from previous step we have to multiply by $\frac{1}{a}$ on both the sides and also division by 0 is undefined i.e ( $\frac{0}{0}→undefined$ )

Hence, the flaw is in the $4^{th}$ step.

Exactly ..

Aditya Sky - 5 years ago

if you liked the solution then do upvote it. :))

Satyabrata Dash - 5 years ago

Upvoted :)

Aditya Sky - 5 years ago

@Aditya Sky – cheers ;))

Satyabrata Dash - 5 years ago

Upvoted :)

Ashish Menon - 5 years ago

@Ashish Menon – thanks.;))

Satyabrata Dash - 5 years ago

(゜-゜) (・o・) (゜o゜) ☺✌✋

Ashish Menon - 5 years ago

☝️=✌️ ;) :)

Satyabrata Dash - 5 years ago

@Satyabrata Dash – Haha (●´ϖ`●) ( ･ิω･ิ) ʕ•ٹ•ʔ

Ashish Menon - 5 years ago

@Ashish Menon – did you like the title?? . i couldnt think of any word so i kept this one

Satyabrata Dash - 5 years ago

@Satyabrata Dash – Haha definitely. I interpreted it as 1 = 2 also.

Ashish Menon - 5 years ago

@Ashish Menon – yep it is 1=2.

Satyabrata Dash - 5 years ago

@Satyabrata Dash – Haha (^_^)

Ashish Menon - 5 years ago

Ashish Menon
May 30, 2016

In fourth step we have cancelled $0$ by $0$ to $1$ which is actually indeterminate. So, the answer is $\color{#69047E}{\boxed{4}}$ .
☺ ☝=✌

☝️=✌️

The answer is 4.

2 solutions

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