### Maths Trivia

See if you can spot what's wrong with these equations...

1)

1)

4 - 10 = 9 - 15

Add 25/4 on both sides

4 - 10 + 25/4 = 9 - 15 + 25/4

(2 - 5/2) (2 - 5/2) = (3 - 5/2) (3 - 5/2)

Taking square roots

(2 - 5/2) = (3 - 5/2)

2 = 3

Can you explain why?

X - Y = 0

Therefore,

2X - 2Y = 0

So,

2X - 2Y = X - Y

2 (X - Y) = (X - Y)

Dividing by (X - Y) on both sides,

2 = 1

Can you explain why?

Add 25/4 on both sides

4 - 10 + 25/4 = 9 - 15 + 25/4

(2 - 5/2) (2 - 5/2) = (3 - 5/2) (3 - 5/2)

Taking square roots

(2 - 5/2) = (3 - 5/2)

2 = 3

Can you explain why?

2)

Let X = YX - Y = 0

Therefore,

2X - 2Y = 0

So,

2X - 2Y = X - Y

2 (X - Y) = (X - Y)

Dividing by (X - Y) on both sides,

2 = 1

Can you explain why?

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Tags: Brain Teasers

Tags: Brain Teasers

## 6 Comments:

for no.2, if (x-y)=0 then, you are dividing both sides by zero which is illegal in mathematics so the equation is false.

I'm too lazy to do manual calculation for no. 1.

OH

MY

GAWD

it's 2:12 AM

MY BRAIN IS FRIED

BUT THANK YOU

FOR THE CHALLENGE

:)

Euian,

You are right about the second one. As for the first one...lol...the answer is there. Just read carefully :D

Jane,

Haha...glad that you are still working ur brains at such an hour. Hope that you find the teasers fun :)

for teaser number 1

the fact is maths is that the square root of a number is always > 0.

hence sqrt(4)=2 and sqrt(9)=3

In puzzle 1....the calculation is perfect all the way till the stage

sqr(2-5/2) = sqr(3-5/2)

now when we take the root of both sides,

sqrt(sqr(3-5/2)) = 3-5/2

but sqrt(sqr(2-5/2)) = 5/2-2 (because 2-5/2 is negative and can't be a result of a sqrt operation.)

You can check for yourself that

5/2 - 2 = 3 - 5/2

Cheers

Aniruddha

for teaser number one aniruddha is wrong since we are not taking square root of any negative number,but of a square whose roots are negative.

for eg.

the sqr root of 1 is -1 or 1;

hence the sqr root of sqr(2-5/2)

can be negative.

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