1=0 ?????????

[dboybbfs]

I have been trying to figure this one out for hours now. The only error I could think of was that you can't divide by an algabraic expression(x-1). Please help!

thank you

Question: Explain what is wrong. Which step(s) are error(s) in and what is the effect of the error(s)?

Let x = 1

then,
step 1: x(x) = 1(x) multiply both sides by x
step 2: x^2-1 = x-1 subtract 1 from both sides
step 3: x^2-1 = x-1 divide both sides by x-1
x-1 x-1
step 4: x+1 = 1 subtract 1 from both sides
-1 -1
step 5: x=0
1=0 ??

 

[Guest]

I have been trying to figure this one out for hours now. The only error I could think of was that you can't divide by an algabraic expression(x-1). Please help!

first off, i don't get why you would do such weird things like multiplying and all that stuff, i guess it's a really weird and ironic question
anyhow
if that's the equation, there's 1 thing i see wrong

well i'll tell you something, you're answer is close but not quiet right
look at the equation closely

x^2-1 = x-1 subtract 1 from both sides
so when you did this, you diviced both sides by x-1

after, you did this :

x^2-1 = x-1 divide both sides by x-1
x-1 x-1

now, watch what happened to your equation


x+1 = 1 subtract 1 from both sides
-1 -1

WHAT HAPPENED THERE?!
look closely and think about the term of dividing
like, try to think about the rule of devision with subtraction and addition equation, THINK!

and also, where the -1 come from in the last step of equation
you said subtract...don't you subtract it to the top? not the buttom?
but yes there's a mistake if i'm not mistakening

if i'm wrong, someone notify me thanks
[/quote]

 

[Mrspi]

I have been trying to figure this one out for hours now. The only error I could think of was that you can't divide by an algabraic expression(x-1). Please help!

thank you

Question: Explain what is wrong. Which step(s) are error(s) in and what is the effect of the error(s)?

Let x = 1

then,
step 1: x(x) = 1(x) multiply both sides by x
step 2: x^2-1 = x-1 subtract 1 from both sides
step 3: x^2-1 = x-1 divide both sides by x-1
x-1 x-1
step 4: x+1 = 1 subtract 1 from both sides
-1 -1
step 5: x=0
1=0 ??

The error is in this step:

You have
(x + 1)(x - 1) = x - 1
And then, you say "divide both sides by (x - 1)"......but in the beginning, it is GIVEN that x = 1. So what is the value of (x - 1)? Can you divide by this??

I hope this helps you.

 

[i.mehrzad]

1=0??

when you wanted to divide the two sides of the equations by x-1, you have to assume that x-1 is not equal to zero.(Reason:Any number on being divided by zero gives an undefined answer)

therefore:
x-1 is not equal to zero
therefore x is not equal to 1.
hence your initial assumption has been contradicted.
Hence your assumption is wrong.
This is my viewing please correct me if i am wrong.[/code]

 

[Guest]

after viewing this, i think the statement of the equation is "false"
if your equation is right
1 = 0 DOES NOT EXIST

 

[ChaoticLlama]

Let x = 1

then,
step 1: x(x) = 1(x)

Unfortunately, you're first step is the error (wrong by assumption). The math you have later on is correct, except that you inadvertantly divided by 0 which is a big problem.

this statement: x(x) = 1(x) is true for x=1.

The important thing to note is that it is true for only x=1.

Think about it logically,

x(x) = 1(x)

Is just a different why of writing

x² = x

Plug in some values

4 = 2
9 = 3
...
100 = 10

That cannot be right.