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16 - 36 = 25 - 45

4^2 - (9x4) = 5^2 -(9x5)

4^2 - (9x4) + 81/4 = 5^2 -(9x5) + 81/4 ......by adding 81/4 to both sides

(4-9/2)^2 = ( 5-9/2)^2......we can cancel the powers on both sides

4- 9/2 = 5- 9/2............add 9/2 to both sides to get:

4=5 !!!

Am I wrong?

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16 - 36 = 25 - 45

4^2 - (9x4) = 5^2 -(9x5)

4^2 - (9x4) + 81/4 = 5^2 -(9x5) + 81/4 ......by adding 81/4 to both sides

(4-9/2)^2 = ( 5-9/2)^2......we can cancel the powers on both sides

4- 9/2 = 5- 9/2............add 9/2 to both sides to get:

4=5 !!!

Am I wrong?

What happened to the underlined parts in the next step?

Edited by Thalia
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You are wrong on the 5th step where you casually mention canceling the powers on both sides!

(-1/2)^2 = (+1/2)^2 does not yield -1/2 = +1/2

But, definitely a good one!

Can't you do it by taking the square root of both sides, which is a "legal" mathematical operation?"

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What happened to the underlined parts in the next step?

This step is legitimate. Think about squaring the term (X-Y). This gives you X^2-2XY+Y^2. In this case X=4 and Y = 9/2 so the square of (4-9/2) = 4^2 -2x4x9/2+(81)/9=4^2-4x9+(81)/4

Can't you do it by taking the square root of both sides, which is a "legal" mathematical operation?"

When youy take the sqareroot, there are 2 possible roots since (-2)^2 and 2^2 both equal 4, when takeing the squareroot, we must consider which root is the appropriate. In this case note that the fith step which currently reads:

4- 9/2 = 5- 9/2

but by choosing the opposite sign on one side, we get instead

9/2-4=5-9/2

which indeed is a true statement since 1/2=1/2

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This step is legitimate. Think about squaring the term (X-Y). This gives you X^2-2XY+Y^2. In this case X=4 and Y = 9/2 so the square of (4-9/2) = 4^2 -2x4x9/2+(81)/9=4^2-4x9+(81)/4

When youy take the sqareroot, there are 2 possible roots since (-2)^2 and 2^2 both equal 4, when takeing the squareroot, we must consider which root is the appropriate. In this case note that the fith step which currently reads:

4- 9/2 = 5- 9/2

but by choosing the opposite sign on one side, we get instead

9/2-4=5-9/2

which indeed is a true statement since 1/2=1/2

The next step would be to take the square root of both sides, but because of examples like the one Peekay gave, you must take the plus or minus square roots of both sides. As someone with some teaching experience in math, this is a common misake of only taking whats known as the&nbsp;&nbsp;&quot;principle&quot; square root (only the positive one) of both sides.<br />

The issue in this case is the the expression on the left (when you said cancel the powers on both sides) (4-9/2)^2 is negative (-0.5 in this case) where as the right (5-9/2)^2 is positive (0.5 in this case).

EDIT: I didnt see the post that explained this already. Sorry for the second posting of the answer... :(

Edited by jaustinsmith_2005
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This same question was found in Prof. Ramanujam's book and here goes the solution

(4-9/2)^2 = (5-9/2)^2

=> 4-9/2 = +/- (5-9/2)

Since 4 is not equal to 5, hence,

4-9/2 = -(5-9/2)

=> 4-9/2 = -5 + 9/2

=> 4+5 = 9/2 + 9/2

=> 9 = 9

Left Hand Side = Right Hand Side

Good luck with your maths exam

I tried to use Spoiler, but it is not working in my machine for reasons i dont know. Hence posted the solution publicly.

Edited by Satish.S
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