+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...
+129840 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 ??
+129840 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.......
+386 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
+129840 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....!!!!!
+386 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
+129840 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 ??
+386 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!
