+0  
 
0
52
2
avatar+10 

Suppose a and x satisfy x^2 + (a - (1/a)) x - 1 = 0. Solve for x in terms of a.

 Dec 28, 2018

Best Answer 

 #1
avatar+3576 
+2

\(x^2 +\left(a - \dfrac 1 a\right)x - 1 = 0\\ \text{let }c = a-\dfrac 1 a\\ \text{using the quadratic formula}\\ x = \dfrac{ -c \pm \sqrt{c^2+4}}{2} = \\ \dfrac{\left(\dfrac 1 a - 1\right)\pm \sqrt{\left(a-\dfrac 1 a \right)^2+4}}{2}\)

 

\(\text{this can be simplified a bit to}\\ x = \dfrac{(1-a) \pm \sqrt{(a-1)^2+4a^2}}{2a}\)

.
 Dec 28, 2018
 #1
avatar+3576 
+2
Best Answer

\(x^2 +\left(a - \dfrac 1 a\right)x - 1 = 0\\ \text{let }c = a-\dfrac 1 a\\ \text{using the quadratic formula}\\ x = \dfrac{ -c \pm \sqrt{c^2+4}}{2} = \\ \dfrac{\left(\dfrac 1 a - 1\right)\pm \sqrt{\left(a-\dfrac 1 a \right)^2+4}}{2}\)

 

\(\text{this can be simplified a bit to}\\ x = \dfrac{(1-a) \pm \sqrt{(a-1)^2+4a^2}}{2a}\)

Rom Dec 28, 2018
 #2
avatar+10 
0

Thank you so much!

sprockit  Dec 30, 2018
edited by sprockit  Dec 30, 2018

28 Online Users

avatar
avatar
avatar

New Privacy Policy

We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive information about your use of our website.
For more information: our cookie policy and privacy policy.