Question

Dada la ecuación: x2
–3x+1=0; si sus raíces es x1 y x2 ;
hallar: E= x1 +x2 + x1 x2 +1

Answer 1

Respuesta:

                      $5$

Explicación paso a paso:

$x^{2} -3x+1 =0$

$a=1; b=-3; c=1$

$Aplicando-la-formula- general:$

$x = \frac{-b\frac{+}{} \sqrt{b^{2}-4ac } }{2a} =\frac{-(-3)\frac{+}{} \sqrt{(-3)^{2} -4(1)(1)} }{2(1)} =\frac{3\frac{+}{}\sqrt{9-4} }{2}$

$x = \frac{3\frac{+}{} \sqrt{5} }{2}$

$x_{1} = \frac{3+\sqrt{5} }{2}$         ;       $x_{2} = \frac{3-\sqrt{5} }{2}$

$E = x_{1} +x_{2} +x_{1} *x_{2} +1$

$E = \frac{3+\sqrt{5} }{2} + \frac{3-\sqrt{5} }{2} +(\frac{3+\sqrt{5} }{2} )*(\frac{3-\sqrt{5} }{2} )+1$

$E = (\frac{3}{2} +\frac{3}{2} )+(\frac{\sqrt{5} }{2} -\frac{\sqrt{5} }{2} )+ (\frac{3}{2})^{2} -(\frac{\sqrt{5} }{2} )^{2} +1$

$E =\frac{6}{2} + 0+ \frac{9}{4} -\frac{5}{4} +1 = 3+0+1+1$

$E = 5$