Say I have 2 quadratics
p(x^2)+qx=r=0 and d(x^2)+ex+f=0 with one common root
can i write (p/d)=(q/e)=(r/f) ?
hey
like comparing coefficients.
can we compare exponents as in this given equation
[(a^n) + (b^n)]/[(a^n-1) + (b^n-1)] = (a+b)/2 (n-1 is exponent)
to get n=1
if yes then what is the condition that allows us to compare?
Well...We can solve this in terms of a and b: b = -a for odd n, so there is no specific relationship needed for n. But generally we can match coefficients of terms on each side of an equation if the terms are members of an orthogonal series. The "power series" is such a series: . Many other orthogonal expansions exist but you'll see the power series the most often.
-Dan