i cant understand how i got the math problem wrong

[lil1ch1ck]

by radical symbol, i mean the square root symbol since i cant put it into the following equation but can u help me solve it & explain why the answer is 3 or 7 since when i solved it myself, i got 9 as an answer.

(radical 2x-5)-(radical x-3)=1

 

[soroban]

Hello, lil1ch1ck!

$\displaystyle \sqrt{2x\,-\,5}\,-\,\sqrt{x\,-\,3}\;=\;1$

Can you explain why the answer is 3 or 7?
When i solved it myself, i got 9 as an answer.

But 9 doesn't check, does it?
You have: $\displaystyle \,\sqrt{2\cdot9\,-\,5}\,-\,\sqrt{9\,-\,3} \:=\:\sqrt{13}\,-\,\sqrt{6}$ . . . which does not equal 1.

You squared illegally, didn't you? *


Isolate a radical: $\displaystyle \,\sqrt{2x\,-\,5}\;=\;\sqrt{x\,-\,3}\,+\,1$

Square both sides: $\displaystyle \,\left(\sqrt{2x\,-\,5}\right)^2\;=\;\left(\sqrt{x\,-\,3}\,+\,1\right)^2$

And we get: $\displaystyle \,2x\,-\,5\;=\;x\,-\,3\,+\,2\sqrt{x\,-\,3}\,+\,1$

$\displaystyle \;\;$which simplifies to: $\displaystyle \,x\,-\,3\;=\;2\sqrt{x\,-\,3}$


Square both sides:\(\displaystyle \,(x\,-\,3)^2\;=\;\left(2\sqrt{x\,-\,3})^2\)

And we get: $\displaystyle \,x^2\,-\,6x\,+\,9\;=\;4(x\,-\,3)$

$\displaystyle \;\;$which simplifies to: $\displaystyle \,x^2\,-\,10x\,+\,21\;=\;0$ . . . a quadratic

$\displaystyle \;\;$which factors: $\displaystyle \,(x\,-\,3)(x\,-\,7)\;=\;0$

$\displaystyle \;\;$and has roots: $\displaystyle \,x\:=\;3,\;7$


Since we squared the equation, we must check for extraneous roots.

And we find that both roots are acceptable.


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*

It is true that: $\displaystyle \,5\,-\,2\;=\;3$

$\displaystyle \;\;$But it is not true that: $\displaystyle \,5^2\,-\,2^2\;=\;3^2$

You cannot run through an expression and square the terms like that.

 

[lil1ch1ck]

wow, thx

yeah sry bout my mistake. i have lots of trouble with the rules since they sometimes get jumbled up in my head. i understand my mistake now. earlier i had asked the same question on yahoo but their explanation was rather confusing & instead of using symbols, they used words. thanks for ur help & for using symbols instead of words. im new to this site so yeah