Question

Given the literal equation xy+x/z=2+z, with y = 4x + 2, what is the value of z if x = 1?

Answer 1

plug y in:

x(4x+2) + x/z = 2+z

plug 1 in for x:

4(1)^2 + 2(1) + 1/z = 2+ z

6 + 1/z = 2 + z

z - 1/z = 4

multiply both sides by z:

z^2 -1 = 4z

\[z ^{2} - 4z -1 = 0\]

use quadratic equation.

\[\frac{ 4\pm \sqrt{(-4)^{2}-4(1)(-1)} }{ 2(1) }\]

z = the resulting 2 terms.