I have a set of equations proving 2=3, please check if it is mathamatically true??

Question

(-6)=(-6)
-10+4= -15+9
add both the side 25/4
-10+4+25/4= -15+9+25/4
(2-5/2)*(2-5/2)=(3-5/2)*(3-5/2)
take positive root on both side
2-5/2=3-5/2
therefore
2=3

Answer 1

False. The fallacious step is where you take the positive root of both sides - just because a²=b² does not mean that a=b. Consider that 1²=(-1)², but 1≠-1. All you can say is that a=±b. Thus your fourth step should be (2-5/2)=±(3-5/2), which becomes -1/2=±1/2, which is true.

Answer 2

How did you get from -10+4+25/4= -15+9+25/4 to (2-5/2)*(2-5/2)=(3-5/2)*(3-5/2...

Here's my solution:

your line:
-10 +4 +25/4 = -15 +9 +25/4

get all in the common denominator 4:
-40/4 + 16/4 +25/4 = -60/4 + 36/4 + 25/4

and add them up for each side:
1/4 = 1/4

Answer 3

Your fine to step 4, step 5 you omit -10 and the -15 without justification. Step 5 should be:
-6+25/4=-6+25/4

Answer 4

The problem is "take positive root of both sides".

This line:
(2-5/2)*(2-5/2)=(3-5/2)*(3-5/2)
yields
(-1/2)^2 = (+1/2)^2
which is still true:
1/4 = 1/4

But when you take the positive root only you neglect the other solution and throw information away. The result is your mis-result of 2=3.


Hope this helps!
The Chicken

Answer 5

If this is so, you should also be able to prove 0=1, since the difference between 2 and 3 is 1, and it would make the equation easier to understand.

Answer 6

not exactly -- the ambiguity in square roots and radicals and solutions to polynomials of degree greater than 1, in general, cannot be removed.

so what you have in effect shown, is that:
sqrt((-1/2)^2) = sqrt((1/2)^2)

(since 2-5/2 = -1/2, 3-5/2 = 1/2)

it's kind of a Galois theory issue with the multiplicity of roots.

Answer 7

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Answer 8

Nope that doesn't work out both in your equation, and it doesn't make sense outside the equation either because two does not equal 3.

Answer 9

the problem is on this line:
(2-5/2)*(2-5/2)=(3-5/2)*(3-5/2)
it is true and equal if solved like this :
(-1/2)*(-1/2) = 1/2*1/2
1/4=1/4
but if squared root, it becomes a complex number (-1)^0,5 or (i)
(-1/2)^0,5 * (-1/2)^0,5 not equals (1/2)^0,5 * (1/2)^0,5
((-1) * 1/2)^0,5 * ((-1) * 1/2)^5 not equals 1/2
(-1)^0,5 x (-1)^0,5 x 1/2 not equals 1/2
(-1)*1/2 not equals 1/2
(-1/2) not equals 1/2

hope it helps

Answer 10

suppose a family consists of three person . father , mother and son . then suppose we killed the son . you say the family will remain the same with it's first situation . is it true ?