Form quadratic equation with roots (alpha² + 1/alpha²) and (beta²+1/beta²)

What equation? Here’s a big tip for you, equations contain an ‘equals sign’ (‘=’) and something that they are equal to. I’m assuming your equation is:

ax2+bx+c=0  

I’m going to use  p  and  q  for the roots of the equation as they are easier to type than  α  and  β . Thus we have:

a(x−p)(z−q)=0⇒ax2−a(p+q)x+apq=0  

Equating coefficients with our initial equation:

x1 :  b=−a(p+q)⇒p+q=−ba  

x0 :  c=apq⇒pq=ca  

Now  p2+q2=p2+2pq+q2−2pq=(p+q)2−2pq  

=(−ba)2−2ca  

=b2a2−2ca  

=b2−2aca2

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