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  • 08-04-2014
  • Mathematics
Answered

What is the solution of the equation?  Eliminate any extraneous solutions.
√3x+28-8=x

 A. 9 and -4
 B. -9 
C. -9 and -4 
D. -4

Verified Answer :

Anonymous Anonymous
  • 08-04-2014

\(\sqrt{3x+28}-8=x\\\\\\A.\ x=9\ \vee\ x=-4\\x=9\to L=\sqrt{3\cdot9+28}-8=\sqrt{27+28}-8=\sqrt{55}-8\\ R=9;\\L eq R\\\\B.\ x=-9\\L=\sqrt{3\cdot(-9)+28}-8=\sqrt{-27+28}-8=\sqrt1-8=1-8=-7;\\ R=-9;\ L eq R\)

\(C.\ x=-9\ \vee\ x=-4\ (see\ B.)\\\\D.\ x=-4\\L=\sqrt{3\cdot(-4)+28}-8=\sqrt{-12+28}-8=\sqrt{16}-8\\=4-8=-4\\R=-4\\L=R\\\\Answer:D.\)

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