• # Maths teacher aroused our curiosity

When studying in school classes one day our Mathematics teacher wrote down a problem on the black board, which aroused our curiosity and also confused us. I recollect here the same;
16 – 36 = 25 – 45 (both differences give the same value – 20)
Add a same constant 81/4 on both sides,
therefore 16 – 36 + 81/4 = 25 – 45 + 81/4
Carefully look at both sides, it is (4 – 9/2)² = (5 – 9/2)² .
Taking square root on both the sides gives 4 – 9/2 = 5 – 9/2.
Now just canceling the common term (-9/2) on both sides we have 4 = 5

How come this?
• I expected that somebody will come forward with the explanation of the error in the steps. But till date none has responded.
T.M.Sankaran
Gold Member, SPK

• Since I have taken up English for my degree course have lost all my touch with maths. I know there is some mistake in this but honestly I have become too weak in maths to figure out what has gone wrong. I'm sure you will provide us the answer too sir.

• It is simple. I was finding the square root of (4 – 9/2)² = (5 – 9/2)². Actually see what is inside the brackets on both sides, Left hand side gives (- 1/2), where as the right hand side is (1/2). So when taking the square root I ignored the sign. So if sign is taken into account, the square root becomes (-(4-9/2)) = (5- 9/2), which when simplified becomes 1/2 = 1/2, which is alright !
T.M.Sankaran
Gold Member, SPK

• Dear sir, I think it's simple as we all know that in any equation we cannot cancel common terms unless and until it is separated by multiplication or division symbol.

• You are not right, cancellation can be done for addition as well as for subtraction. In the above example, perhaps you are referring to the cancellation of (- 9/2) on both sides of 4 – 9/2 = 5 – 9/2.It is possible because the cancellation here simply means taking one of the (-9/2) to the other side. Then it becomes +9/2. So on one side we get - 9/2 +9/2 which is equal to zero. That is cancellation here.
T.M.Sankaran
Gold Member, SPK

• ok sir

• Oh nice thread. Thanks for the useful information to share with us. I am also struggling with many problems with this. But I cannot find its answer corrects. Many of them are avoid simple conditions. I know this method and how to solve. But some times forgot it. Any may thanks for theread and comments.
Regards
SULTHAN

• hiii...
i am new to this forum

• hiii...
Well this is quite useful site for particular forum.Yes its true that some maths teachers aroused our curiosity.But of anyone need to have an expert advice i would rather request to have a look to...

• It is a nice observation. There are lots of tricky questions and fun stuffs in mathematics subject. Here this small error is due to lack of a negative sign as explained by T.M.Sankaran sir. When ever we take a square root of some value ( let it be X), then it will have two values which we cannot predict in this case. That is,

sq.root of (X^2) = + or - (X)