Given that the graph of function f(x)=(a x+ x+1)(x+ x+1)(a R) has at least 3 intersection points with the graph of function g(x)=x^2 , find the value of k for which a > k*(e^2)/8.

Step-by-step solution

aligned f(x) & =g(x) x^2 & = (a+ x+1 x ) (1+ x+1 x ) Put x+1 x & =t (a+t)(1+t) & =1 F(t)+t^2+(a+1) t+a-1 & =0 aligned For 3 solutions, one solution in (- , 0) and another solution in aligned & F(0) 0 & a -1 2 & a ( -1 2 , 1 ) aligned [Note: If F(t) has 4 solutions than that case is rejected (think)]