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?
All Replies (10)
Cijo George Thomas
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)
sq.root of (X^2) = + or - (X)
shaunn
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...
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...
SULTHAN
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.
T.M.Sankaran
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.
JEENA S SUBRAMONIAM
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.
T.M.Sankaran
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 !
Gayathri.Jayakumar
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.
T.M.Sankaran
I expected that somebody will come forward with the explanation of the error in the steps. But till date none has responded.
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