SOLUTION: how would you solve for x in this equation: 3x + xSR3 = 3 + 3SR3 I'm studying for the GMAT and one practice book had this question but didn't give anything but the solution (x=

Algebra ->  Algebra  -> Square-cubic-other-roots -> SOLUTION: how would you solve for x in this equation: 3x + xSR3 = 3 + 3SR3 I'm studying for the GMAT and one practice book had this question but didn't give anything but the solution (x=      Log On

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Question 133322: how would you solve for x in this equation:
3x + xSR3 = 3 + 3SR3
I'm studying for the GMAT and one practice book had this question but didn't give anything but the solution (x=SR3) and it has been bugging me something terrible.
Thanks.

Answer by Edwin McCravy(6939) About Me  (Show Source):
You can put this solution on YOUR website!
how would you solve for x in this equation:
3x+%2B+x%2Asqrt%283%29+=+3+%2B+3sqrt%283%29
I'm studying for the GMAT and one practice book had this question but didn't give anything but the solution (x=sqrt%283%29) and it has been bugging me something terrible.
 
Factor x out on the left side:
 
x%283+%2B+sqrt%283%29%29+=+3+%2B+3%2Asqrt%283%29
 
Divide both sides by %283+%2B+sqrt%283%29%29
 
%0D%0A%28x%283+%2B+sqrt%283%29%29%29%0D%0A%2F%28%283%2Bsqrt%283%29%29%29%0D%0A+=+%0D%0A%283+%2B+3%2Asqrt%283%29%29%0D%0A%2F%28%283%2Bsqrt%283%29%29%29%0D%0A
 
Cancel on the left:
 
%0D%0A%28x%28cross%283+%2B+sqrt%283%29%29%29%29%0D%0A%2F%28%28cross%283%2Bsqrt%283%29%29%29%29%0D%0A+=+%0D%0A%283+%2B+3%2Asqrt%283%29%29%0D%0A%2F%28%283%2Bsqrt%283%29%29%29%0D%0A
 
%0D%0Ax+=+%0D%0A%283+%2B+3%2Asqrt%283%29%29%0D%0A%2F%28%283%2Bsqrt%283%29%29%29%0D%0A
 
Put parentheses around the top because we
are going to be multiplying:
 
%0D%0Ax+=+%0D%0A%28%283+%2B+3%2Asqrt%283%29%29%29%0D%0A%2F%28%283%2Bsqrt%283%29%29%29%0D%0A
 
Rationalize the denominator by multiplying
by the conjugate of the denominator over
itself.  That is, multiply by %28%283-sqrt%283%29%29%29%2F%28%283-sqrt%283%29%29%29%29, which
can't affect the value since it equals 1.
 
x+=+%0D%0A%28%283+%2B+3%2Asqrt%283%29%29%29%0D%0A%2F%28%283%2Bsqrt%283%29%29%29%0D%0A%28%283-sqrt%283%29%29%29%2F%28%283-sqrt%283%29%29%29%29
 
%0D%0Ax+=+%0D%0A%28++%283+%2B+3%2Asqrt%283%29%29%283-sqrt%283%29%29+++++++++%29%0D%0A%2F%28+%283%2Bsqrt%283%29%29%283-sqrt%283%29%29++%29%0D%0A
 
Now use the "FOIL" principle on the
top and bottom:
 
x+=+%289-3%2Asqrt%283%29+%2B9%2Asqrt%283%29+-+3%2A%28sqrt%283%29%29%5E2%29%0D%0A+%0D%0A%2F%289-3%2Asqrt%283%29%2B3%2Asqrt%283%29+-+%28sqrt%283%29%29%5E2%29
 
Combine the two middle terms in the top:
 
x+=+%289%2B6%2Asqrt%283%29+-+3%2A%28sqrt%283%29%29%5E2%29%0D%0A+%0D%0A%2F%289-3%2Asqrt%283%29%2B3%2Asqrt%283%29+-+%28sqrt%283%29%29%5E2%29
 
The middle two terms on the bottom cancel:
 
x+=+%289%2B6%2Asqrt%283%29+-+3%2A%28sqrt%283%29%29%5E2%29%0D%0A+%0D%0A%2F%289-cross%283%2Asqrt%283%29%2B3%2Asqrt%283%29%29+-+%28sqrt%283%29%29%5E2%29
 
x+=+%289%2B6%2Asqrt%283%29+-+3%2A%28sqrt%283%29%29%5E2%29%0D%0A+%0D%0A%2F%289+-+%28sqrt%283%29%29%5E2%29
 
Replace %28sqrt%283%29%29%5E2 by 3
 
x+=+%289%2B6%2Asqrt%283%29+-+3%2A3%29%0D%0A+%0D%0A%2F%289+-+3%29
 
x+=+%289%2B6%2Asqrt%283%29+-+9%29%0D%0A+%0D%0A%2F6
 
x+=+%286%2Asqrt%283%29%29%0D%0A+%0D%0A%2F6
 
Cancel the 6's
 
x+=+%28cross%286%29%2Asqrt%283%29%29%0D%0A+%0D%0A%2Fcross%286%29

x+=+sqrt%283%29

Edwin