Question

solve the proportion for x. (x+4)/(2)=(4)/(x). What is the larger solution? What is the smaller solution?

Answer 1

\[\frac{x+4}{2}=\frac{4}{x}\]
\[x(x+4)=8\]
\[x^2+4x=8\]
\[x^2+4x-8=0\]
\[x=\frac{-4\pm \sqrt{4^{2}-4(1)(-8)}}{2(1)}=\frac{-4\pm \sqrt{48}}{2}\]

Answer 2

\[x=\frac{-4\pm 4\sqrt{3}}{2}=-2\pm2\sqrt{3}\]

Answer 3

The larger root is
\[-2+2\sqrt{3}\]

Answer 4

The smaller root is
\[-2-\sqrt{3}\]