#1
Yeah, im sorry for another of these threads, but i desperately need some help. Im a pretty good math student for my level (10th grade), but i just couldnt get this.
Today in class, the teacher gave a sum, and while we were doing it, she walks up to me and gives me this sum to do.
I spent like 2 hours trying this sums using different methods, but just couldnt get it. So any help is appreciated!

(4-x)^1/2 + (x-2)^1/2 = x^2 -6x +11
OR
Root of (4-x) + Root of (x-2)= x^2 -6x +11

Im sure its irrational or imaginary. Thanks again!
#2
I'm assuming you're solving for x?
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#4
You should try completing the square.
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#7
x = 3

LHS= (4-3)^1/2 + (3-2)^1/2

(4-3)^1/2 = 1
(3-2)^1/2 = 1
1+1 = 2

RHS = 3^2 - 6(3) + 11

9 - 18 + 11
- 9 + 11
2

Final 2 = 2
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#8
Quote by Cha0sThe0ry
x = 3

...

Final 2 = 2

You don't solve maths by guessing numbers and seeing if they fit.
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#10
are you sure you wrote the problem out right ?
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#11
Quote by Deliriumbassist
Yeah you can, it's called trial and error

And how many points do you think you'll get if you do that on, say, an exam?

Hint: answer < 1
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#12
the best way is to graph both equations and see where they intersect.
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#13
Quote by Deliriumbassist
Yeah you can, it's called trial and error



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#14
or square both sides, the x's on the LHS drop, and solve for x on the right side
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#15
Quote by Raziel2p
And how many points do you think you'll get if you do that on, say, an exam?

Hint: answer < 1


At GCSE level you can get away with it. Which is grade 10 (roughly). In the UK, at GCSE or lower, full credit has to be awarded if the answer is correct.

at A-Levels, not so much.
#16
I didnt copy the equations, she wrote it down for me. So i doubt she made a mistake. And yeah, i got 3 as an answer as well, but figured there are more than one solutions.
And ive tried squaring everything, etc. etc. Aint work.
Any other help?
#17
Quote by Raziel2p
You don't solve maths by guessing numbers and seeing if they fit.


Oh no ****?

(4-x)^1/2 + (x-2)^1/2 = x^2 -6x +11

(4-x)^1/2 + (x-2)^1/2 - 11 = x^2 -6x

(4-x)^1/2 + (x-2)^1/2 -11 -x^2 = -6x

((4-x)^1/2 + (x-2)^1/2 -11 -x^2) / x = -6

- ((4-x)^1/2 + (x-2)^1/2 -11 -x^2) / x) = 6

Now the only reasonable answer would be 3 wouldnt it?
So i based my answer on math I didnt just plug in numbers and chug out the anwers. It just worked out so I didnt have to do any more math



Oh and this would get full credit on say, an exam.
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#18
The only reasonable answer? Isn't that the same as guessing and seeing if it fits? I'd love to see how you're capable of doing the rest of the equation, let alone in your head.
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#19
Quote by Cha0sThe0ry
Oh no ****?

(4-x)^1/2 + (x-2)^1/2 = x^2 -6x +11

(4-x)^1/2 + (x-2)^1/2 - 11 = x^2 -6x

(4-x)^1/2 + (x-2)^1/2 -11 -x^2 = -6x

((4-x)^1/2 + (x-2)^1/2 -11 -x^2) / x = -6

- ((4-x)^1/2 + (x-2)^1/2 -11 -x^2) / x) = 6

Now the only reasonable answer would be 3 wouldnt it?
So i based my answer on math I didnt just plug in numbers and chug out the anwers. It just worked out so I didnt have to do any more math



Oh and this would get full credit on say, an exam.


You're still guessing at that point. You didn't solve for the variable.
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#20
Similar but not the same if you have a number that fits based on math how is that not excepted? Try and solve the problem yourself mr "high and mighty". M'kay pumpkin?
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#21
Quote by Cha0sThe0ry
Similar but not the same if you have a number that fits based on math how is that not excepted? Try and solve the problem yourself mr "high and mighty". M'kay pumpkin?

Ah, so until I can find a solution that fits, yours is correct? Asshat. And if you're serious about that kind of answer passing on an exam, US education is really poor compared to Norwegian. When you're dealing with equations, you can find the answer and prove it's right, but you won't get full score if you don't show how to work out the answer.

And no, I don't know how to work it out.
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#22
Quote by Raziel2p
Ah, so until I can find a solution that fits, yours is correct? Asshat. And if you're serious about that kind of answer passing on an exam, US education is really poor compared to Norwegian. When you're dealing with equations, you can find the answer and prove it's right, but you won't get full score if you don't show how to work out the answer.

And no, I don't know how to work it out.


Well, yeah. In proof mathematics, I had to solve things by trying to prove them wrong. I can't remember the latin term though.
#23
Quote by Raziel2p
You don't solve maths by guessing numbers and seeing if they fit.


You do in solving differential equations. Then it's the only accepted way of solving problems.