Question

What type is of the set A = {2, 3} and B = {x: x is solution of x2 - 5x + 6 = 0} ?

Answer 1

Answer:

$x^2-5x+6=0\quad :\quad x=3,\:x=2$

Step-by-step explanation:

$x^2-5x+6=0$

$x_{1,\:2}=\frac{-\left(-5\right)\pm \sqrt{\left(-5\right)^2-4\cdot \:1\cdot \:6}}{2\cdot \:1}$

$x_{1,\:2}=\frac{-\left(-5\right)\pm \:1}{2\cdot \:1}$

$\mathrm{Separate\:the\:solutions}$

$x_1=\frac{-\left(-5\right)+1}{2\cdot \:1},\:x_2=\frac{-\left(-5\right)-1}{2\cdot \:1}$

$\frac{-\left(-5\right)+1}{2\cdot \:1}$

$=\frac{5+1}{2\cdot \:1}$

$\mathrm{Add\:the\:numbers:}\:5+1=6$

$=\frac{6}{2\cdot \:1}$

$=\frac{6}{2}$

$=3$

$\frac{-\left(-5\right)-1}{2\cdot \:1}$

$=\frac{5-1}{2\cdot \:1}$

$=\frac{4}{2\cdot \:1}$

$=\frac{4}{2}$

$=2$

$\mathrm{The\:solutions\:to\:the\:quadratic\:equation\:are:}$

$x=3,\:x=2$