Answer:
=-0.809
Step-by-step explanation:
3x^2+5x+7=0 complete the square
3x^2+5x=-7 divide both sides by 3
x^2+5/3 x = -7/3 to complete the square add term(b/2)^2=((5/3)/2)²=25/36
X^+5/3 x+25/36=-7/3 +25/36 factorize
(x+5/6)²= -59/36
x+5/6= + or - √59/36
solution for x= -5/6-√59/6i (u) OR -5/6+√59/6i (v)
u/v + v/u=(-5/6-√59/6i)/(-5/6+√59/6i) +(-5/6+√59/6i)/(-5/6-√59/6i)=-17/21
=-0.809
Answer:
[tex]\large \boxed{\sf \ \ \ -\dfrac{17}{21}=-0.80952... \ \ \ }[/tex]
Step-by-step explanation:
Hello,
First of all we can verify that 0 is not a solution of the equation so that we can divide by u or v
[tex]\dfrac{v}{u}+\dfrac{u}{v}=\dfrac{u^2+v^2}{uv}=\dfrac{(u+v)^2-2uv}{uv}=\dfrac{(u+v)^2}{uv}-2[/tex]
And we know that
[tex]u+v=-\dfrac{5}{3}\\\\uv=\dfrac{7}{3}\\\\\\as \ \ (x-u)(x-v)=x^2-(u+v)x+uv[/tex]
So it comes
[tex]\dfrac{v}{u}+\dfrac{u}{v}=\dfrac{5^2*3}{7*3^2}-2=\dfrac{25-42}{21}=-\dfrac{17}{21}=-0.80952...[/tex]
Hope this helps.
Do not hesitate if you need further explanation.
Thank you
