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# Quick maths question c3 Factorising HELP please watch

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1. Say you have 2+x^1/2 = x (2 plus square root of x equals x)
if I square the whole equation in attempt to get rid of the square root I get 4+x=x^2 and then rearranging this give x^2 - x -4=0 However this gives me the wrong solution.
Even substituting x^1/2 as u gives 2+u=u^2 which again gives me the wrong solutions... what is the reason for this?? Because I'm so confused - the way to do it is moving the 2 over to the other side first to get x^1/2 = x-2 and then squaring to get x=(x-2)^2 and solving this gives me the correct answer but I don't understand how Im meant to know which order to go in - isnt this question just BIDMAS backwards?? and the squareroot is basically an indice of 1/2??

Any help would mean the most

This is also like substituting x^1/2 as u.
2. (Original post by MrToodles4)
Say you have 2+x^1/2 = x (2 plus square root of x equals x)
if I square the whole equation in attempt to get rid of the square root I get 4+x=x^2 and then rearranging this give x^2 - x -4=0 However this gives me the wrong solution.
Even substituting x^1/2 as u gives 2+u=u^2 which again gives me the wrong solutions... what is the reason for this?? Because I'm so confused - the way to do it is moving the 2 over to the other side first to get x^1/2 = x-2 and then squaring to get x=(x-2)^2 and solving this gives me the correct answer but I don't understand how Im meant to know which order to go in - isnt this question just BIDMAS backwards?? and the squareroot is basically an indice of 1/2??

Any help would mean the most

This is also like substituting x^1/2 as u.
You're squaring the LHS wrong in the first attempt.

Substituting u in is probably the best way to do it. Solve 2+u=u^2 for u (Like you would solve a normal quadratic) and then that'll work.
3. (Original post by MrToodles4)
Say you have 2+x^1/2 = x (2 plus square root of x equals x)
if I square the whole equation in attempt to get rid of the square root I get 4+x=x^2
No you dont. You get - expand the LHS.

Replace with in the expanded form, simplifying it gives you the 'correct' form
4. (Original post by MrToodles4)
Say you have 2+x^1/2 = x (2 plus square root of x equals x)
if I square the whole equation in attempt to get rid of the square root I get 4+x=x^2 and then rearranging this give x^2 - x -4=0 However this gives me the wrong solution.
Even substituting x^1/2 as u gives 2+u=u^2 which again gives me the wrong solutions... what is the reason for this?? Because I'm so confused - the way to do it is moving the 2 over to the other side first to get x^1/2 = x-2 and then squaring to get x=(x-2)^2 and solving this gives me the correct answer but I don't understand how Im meant to know which order to go in - isnt this question just BIDMAS backwards?? and the squareroot is basically an indice of 1/2??

Any help would mean the most

This is also like substituting x^1/2 as u.
2+x^1/2 doesn't give 4+x - remember (2+x^1/2)(2+x^1/2) its kinda like a quadratic u should have 3 terms
5. (Original post by JammieDodger27)
You're squaring the LHS wrong in the first attempt.

Substituting u in is probably the best way to do it. Solve 2+u=u^2 for u (Like you would solve a normal quadratic) and then that'll work.
Thank youuu
6. (Original post by RDKGames)
No you dont. You get - expand the LHS.

Replace with in the expanded form, simplifying it gives you the 'correct' form
7. (Original post by MrToodles4)
Why doesn't submitting for 'u' work??
It does.

Solve it for , then square the expression to get x since u is just root x.
8. move 2 to the other side and use your method and you get x = (x-2)^2 (I think you know what (x-2)^2 equals to), move all the terms on one side , solve the resulting quadratic equation
9. (Original post by RDKGames)
It does.

Solve it for , then square the expression to get x since u is just root x.
Thanks I realised - so it is an incorrect method to move the 2 over to the other side and then square?? (x-2)^2 because I get a different different answer doing it that way.
10. (Original post by MrToodles4)
Thanks I realised - so it is an incorrect method to move the 2 over to the other side and then square?? (x-2)^2 because I get a different different answer doing it that way.
It's still correct. Dunno where you're going wrong.
11. (a+b)(a+b) = a^2 + 2ab + b^2

Does this help?

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Updated: October 15, 2017
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