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1 = 1 {a simple fact}

(1)^2 = (-1)^2 {squaring both sides (square of -1 is also 1) }

1 = -1 {taking root on both sides}

(1) +4 = (-1) +4 {adding a constant 4 on both sides}

5 = 3 {by simple addition}


CAN YOU FIND ANY WRONG IN THIS ?

2007-12-07 18:54:51 · 19 answers · asked by Anonymous in Science & Mathematics Mathematics

in 3rd line i am removing squares on both sides

like
(x)^2 = (y)^2
and hense
x=y

2007-12-07 19:05:42 · update #1

19 answers

if you select ONE of the two possible values for the square root solution then you have to stick to it through out.
it is true that the square root of 1 is both 1 and/or -1 ... it is not true however that the two results of a square root are equal.
You COULD say;
√(1) +4 = √(1) +4 [which implies (±1 +4) = (±1+4) and nothing else]
OR
(-1)^2 +4 = 1^2 +4

2007-12-07 19:12:55 · answer #1 · answered by David F 5 · 3 1

Lots of good answers. Keep in mind that when you take the square root you are actually finding solutions to a simple polynomial.

When you ask:
What is the square root of z? What is meant is
find x such that x^2=z. There are two solutions. When z=1 the two solutions are +1 and -1.

It's also important to realize that when you square an equation you introduce new solutions. For example

The equation x-1=0 has the solution x=1. But when you square the equation x=1 you get x^2=1 or x^2-1=0 which factors into (x-1)(x+1)=0 having the obvious solutions.

You'll learn this stuff when you get to complex numbers.

Start with x=1, now raise both sides to the k power where k is a postive integer. Then the equation x^k-1=0 has k complex roots called 'the k roots of unity'. When k=2 you get the two real roots already discussed. For any larger value of k you get mostly complex valued roots.

Have fun! Oh, I almost forgot to remind you not to divide by zero. If too many attempts are to divide by zero then gravity will reverse and we'll all go flying off the earth into space.

2007-12-08 03:16:42 · answer #2 · answered by modulo_function 7 · 0 0

when you do this
you come up with multiple solutions
as you can with a quadratic or cubic equations
some are real, some are not
the solutions
1 = 1 , -1 = -1
are real

and the solutions
-1 = 1
1 = -1
are non-real (extranneos)

Therefore yes, 5 = 3 by definition
however because 1 = -1 as well
i can take the square root of both sides
saying that
1 = i
or
-1 = i
but i is nonreal and 1 is
so neither are 5 and 3

so pretty much
next time you have 5 cookies
im gonna take 2
and say that 5 = 3
so u have the same number of cookies

2007-12-08 03:14:43 · answer #3 · answered by Mr. Edd 1 · 1 0

When you take the square root of both sides of an equation, it is possible to introduce extraneous solutions. That is precisely what goes wrong here.

When you take the square root of both sides, you can have one of the following four possibilities:

1 = 1
-1 = -1
1 = -1
-1 = 1

Only the first two make sense, the last two are nonsense.

2007-12-08 03:00:24 · answer #4 · answered by Chris W 4 · 4 0

well, the square root of a negative number is an imaginary number, not 1.
(1)+4 = 5 while (-1)+4 = 3
i am pretty sure 5 does not =3

could you explain you reasoning behind the bottom 2 statements? im not seeing it.

2007-12-08 03:00:17 · answer #5 · answered by pyr032486 2 · 1 0

When you take the root of both sides it will be equal to (+or-) 1. Ur taking the sqrt of both sides, and when you take the sqrt. of a positive number it will give you an answer that is (+or-).
So the third line is suppose to read
(+or-) 1= (+or-) 1 {taking root on both sides}.

At least that's the best I can come up with.

2007-12-08 03:05:15 · answer #6 · answered by Jeremy B 2 · 2 0

You say that x^2 = y^2 implies x =y.

This is incorrect logic. The reason? it is because the function f(t) = t^2 is not a one-to-one function (i.e. its graph doesnt pass the horizontal line test). Why is this important? Because it means you could have two different inputs that yield the same output. (like -1 and 1)

Only one to one functions allow the logical conclusion that if f(x) = f(y), then x = y

2007-12-08 03:33:18 · answer #7 · answered by Steve 5 · 0 0

This is a typical maths problem.

One fact is square root 1 is modulus of 1.

It may be +1 or -1.
OR has lots of meaning.
It does not say +1 and -1.


Same is problem in your case here.
Thank you.

2007-12-08 03:01:32 · answer #8 · answered by Anonymous · 2 0

(-1)^2 = 1,

2007-12-08 03:02:40 · answer #9 · answered by iceman 7 · 0 1

in the 2nd line, the square root of (-1)^2 is not -1. its equal to 1

2007-12-08 03:00:55 · answer #10 · answered by carolmhamilton 2 · 0 2

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