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avatar+386 

sqrt (k + x ) + sqrt(x) - 7 = 0

 

I went:

 

sqrt(x) - 7 = - sqrt(k+x)

 

but now I'm stuck because if I do ^2 on both sides I don't know if I get:

 

x + 49 = -k - x

 

OR

 

x+49 = k + x

 

I know it's pretty basic stuff but the calculators solve this confuses me because of the syntax...

 Dec 18, 2016

Best Answer 

 #5
avatar+129849 
+5

Awesome!

 

Could you just explain to me how you go from:

 

 

sqrt (k + x ) = 7  - sqrt(x)   square both sides

 

to

 

k + x  =     49   -  14 sqrt(x) +  x  

 

+++++++++++++++++++++++++++++++++++++++++++++++++++++++

 

OK.....squaring both sides, we have

 

(√( k + x) )^2  = ( 7  - √x)^2      [squaring the left side just causes the radical to disappear]

 

k + x  =  ( 7  - √x) ( 7  - √x)    expand on the right

 

k + x  =  49  - 7√x  - 7√x  + x

 

k + x  =  49  - 14√x    + x   

 

Does that help ??

 

 

cool cool cool

 Dec 18, 2016
 #1
avatar+129849 
0

sqrt (k + x ) + sqrt(x) - 7 = 0

 

Note, Tony.......there are  infinite things that might work, here.....because we have more variables than equations......for example...

 

k = 49    and x  = 0

sqrt (49 + 0 ) + sqrt(0) - 7 = 0

sqrt (49 ) + 0  - 7 = 0

7 + 0 - 7   = 0

 

or

 

k = 7  and x = 9

sqrt (7 + 9 ) + sqrt(9) - 7 = 0

sqrt (16) + sqrt(9) - 7 = 0

4   +  3    - 7 =  0

7  - 7 = 0

 

etc  .......

 

 

This willl always happen whenever we have more variables than equations.......

 

 

 

cool cool cool

 Dec 18, 2016
 #2
avatar+386 
0

Here is the exact problem given in my class:

 

"Resolve in X":

 

sqrt (k + x) + sqrt (x) - 7 = 0

 

Now here is the answer provided by the book:

 

( k^2 - 98k + 2401 ) / 196    where k ∈ R

TonyDrummer2  Dec 18, 2016
 #3
avatar+129849 
+5

OK...I see....let me get you there

 

sqrt (k + x ) + sqrt(x) - 7 = 0     rearrange

 

sqrt (k + x ) = 7  - sqrt(x)   square both sides

 

k + x  =     49   -  14 sqrt(x) +  x        subtract x from both sides

 

k = 49  -  14 sqrt(x)   rearrange

 

14 sqrt(x)  =  49  - k  square both sides

 

196x  =  2401  - 98k + k^2     divide both sides by 196

 

x  = [2401  - 98k + k^2] / 96  =  [ k^2 - 98k + 2401] / 96 

 

Voila....!!!!!

 

 

 

cool cool cool

 Dec 18, 2016
 #4
avatar+386 
0

Awesome!

 

Could you just explain to me how you go from:

 

 

sqrt (k + x ) = 7  - sqrt(x)   square both sides

 

to

 

k + x  =     49   -  14 sqrt(x) +  x  

 

I don't get how  ( - sqrt (x)  )^2  =  -14sqrt(x) + x

TonyDrummer2  Dec 18, 2016
 #5
avatar+129849 
+5
Best Answer

Awesome!

 

Could you just explain to me how you go from:

 

 

sqrt (k + x ) = 7  - sqrt(x)   square both sides

 

to

 

k + x  =     49   -  14 sqrt(x) +  x  

 

+++++++++++++++++++++++++++++++++++++++++++++++++++++++

 

OK.....squaring both sides, we have

 

(√( k + x) )^2  = ( 7  - √x)^2      [squaring the left side just causes the radical to disappear]

 

k + x  =  ( 7  - √x) ( 7  - √x)    expand on the right

 

k + x  =  49  - 7√x  - 7√x  + x

 

k + x  =  49  - 14√x    + x   

 

Does that help ??

 

 

cool cool cool

CPhill Dec 18, 2016
 #6
avatar+386 
+5

My bad, didn't picture it this way in my mind.

 

I already know this, don't know why I didn't think of it that way on this one...

 

Thanks!

TonyDrummer2  Dec 18, 2016

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