Math question which I am confused about (1 Viewer)

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Hey BOS,

I need help with a math question.

The question was to solve:

1+x^(-1/2)=0

I did all the working out and got to the step where:

sqrt(x)=-1

And I know that there is no real solutions. But then I went and did this,

x=(-1)^2
= 1

I know x = 1 is wrong because if you sub it back it wont work, but I dont get what is wrong with my steps though because they seem fine to me.

Please explain clearly to me because it's very confusing.

 

[Zenox]

No solution

1 + x^(-1/2) = 0

x^(1/2) = -1 , x=>0

therefore no solution

 

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I know the answer is no solution but when I mucked around with the equation I got x = 1 (which is wrong).

I just need someone to justify why my steps leading to x =1 is incorrect because all the steps seem fine to me at this point.

Where's carrotsticks when you need him! Spiral! Drongoski (I hope I spelt it right)!!

 

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Anyone? Please, this question is bugging me! haha

 

[AAEldar]

No solution.

Not sure how you got x=1.. but if you sub that in the original expression you don't get a valid answer.

 

[seanieg89]

 

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Oh...then what does ] equal to?

 

[Sy123]

Oh...then what does ] equal to?

 

[SunnyScience]

Note:

=

 

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Does that relate to the absolute value function?

Is it true to say ?

 

[SunnyScience]

Does that relate to the absolute value function?

Is it true to say ?

Nvm. I'm retarded. ~~~~those moments~~~~
Don't judge me.

 

[seanieg89]

Actually, I apologise, what I meant to say was that

does NOT imply that .

So you cant just square both sides of an equation you are trying to solve in general, you will add "fake" solutions.

 

[SunnyScience]

Does that relate to the absolute value function?

Is it true to say ?

Sorry, ignore my original addition. What I said is completely wrong, I confused the position of the square.

 

[bobmcbob365]

Well, put simply, by squaring both sides, you're effectively changing the equation to whole new different equation.

For example, consider the equation x=1.
Now, this is the same as asking where on the Cartesian plane, does the line y=x intersect with the line y=1.
Now obviously, there's only one solution, because y=x is a straight line.

If you square both sides, you get x^2 =1.
Now, when you picture the curve y=x^2 and y=1. You realise that they intersect at two points, i.e. x = 1 and x = -1.

This is because you are effectively changing the goal you're trying to achieve.

When, you square both sides, you're mutating your original goal (of finding the points of intersection between y=x and y=1) into a similar goal (of finding the points of intersection between y=x^2 and y=1)


However, the reason we can rely on squaring both sides as a method of solving equations in most cases, is because this "similar" graph or goal has "similar" solutions or answers to their goals. But we get the right answers most of the time because we're just simply lucky that this "similar" goal has the "same" solutions.

This is why many regard 'squaring both sides' a dangerous thing to do in maths.

Here's another example:
when you were taught how to solve inequalities such as 1/x < x
One of the methods was to square both sides, in order to deal with the fact that the denominator might be negative. This, in fact, is changing the question and dealing with another question, but dealing with a "similar" question, and so you are able to get "similar" answers.

The Cambridge textbook deals with it briefly in the Year 12 textbook page 51.

 

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Actually, I apologise, what I meant to say was that

does NOT imply that .

So you cant just square both sides of an equation you are trying to solve in general, you will add "fake" solutions.

Actually, I apologise, what I meant to say was that

does NOT imply that .

So you cant just square both sides of an equation you are trying to solve in general, you will add "fake" solutions.

Hey Seanieg89, i sort of starting to get your explanation but can you show me an example so I can get it? I think i know what you are saying but can you explain using the question i posted up and tell me why my steps are wrong?

 

[seanieg89]

You can think of a mathematical argument as a chain of logic, a bunch of facts connected by logical steps.

Eg/

x^2+2x+1=0

=> (x+1)^2=0

=> x+1=0

=> x=-1.

All we have shown here is that any solution to the original equation must be -1. This does NOT necessarily mean that -1 IS in fact a solution of the original equation. For this to be true, all of our logical steps must be reversable. (In this case they are). But the act of squaring both sides of x=a is NOT reversible if a is nonzero, because for example, -1 is a solution to x^2=1^2 but is not a solution to x=1.

A more everyday example of this idea is the fact that the two following sentences are very different in meaning:

"Every person who does mathematics is sexy".

"Every sexy person does mathematics".

 

[-Dark Light-]

You can think of a mathematical argument as a chain of logic, a bunch of facts connected by logical steps.

Eg/

x^2+2x+1=0

=> (x+1)^2=0

=> x+1=0

=> x=-1.

All we have shown here is that any solution to the original equation must be -1. This does NOT necessarily mean that -1 IS in fact a solution of the original equation. For this to be true, all of our logical steps must be reversable. (In this case they are). But the act of squaring both sides of x=a is NOT reversible if a is nonzero, because for example, -1 is a solution to x^2=1^2 but is not a solution to x=1.

A more everyday example of this idea is the fact that the two following sentences are very different in meaning:

"Every person who does mathematics is sexy".

"Every sexy person does mathematics".QUOTE]

LOL.....THanks I get it now!!

Also thansk to everyone else!

 

[-Dark Light-]

Well, put simply, by squaring both sides, you're effectively changing the equation to whole new different equation.

For example, consider the equation x=1.
Now, this is the same as asking where on the Cartesian plane, does the line y=x intersect with the line y=1.
Now obviously, there's only one solution, because y=x is a straight line.

If you square both sides, you get x^2 =1.
Now, when you picture the curve y=x^2 and y=1. You realise that they intersect at two points, i.e. x = 1 and x = -1.

This is because you are effectively changing the goal you're trying to achieve.

When, you square both sides, you're mutating your original goal (of finding the points of intersection between y=x and y=1) into a similar goal (of finding the points of intersection between y=x^2 and y=1)


However, the reason we can rely on squaring both sides as a method of solving equations in most cases, is because this "similar" graph or goal has "similar" solutions or answers to their goals. But we get the right answers most of the time because we're just simply lucky that this "similar" goal has the "same" solutions.

This is why many regard 'squaring both sides' a dangerous thing to do in maths.

Here's another example:
when you were taught how to solve inequalities such as 1/x < x
One of the methods was to square both sides, in order to deal with the fact that the denominator might be negative. This, in fact, is changing the question and dealing with another question, but dealing with a "similar" question, and so you are able to get "similar" answers.

The Cambridge textbook deals with it briefly in the Year 12 textbook page 51.

OOO Thanks for the page reference! I get it now, cheers!

 

[seanieg89]

No worries, glad to help.