Home › Forums › Math questions › Algebra questions

A tough problem for me , need help!

Posted May 7th, 2009 by alpha
in

If each pair of 3 equations $ x^2+p_1x+q_1=0 $,$ x^2+p_2x+q_2=0 $&$ x^2+p_3x+q_3=0 $ have a common root , then prove that $ p_1 ^2+ p_2 ^2+p_3 ^2+4(q_1+q_2+q_3)=2(p_1p_2+p_2p_3+p_3p_1) $

‹ Inequality Inequality Type-2 ›

Comments

answer

On May 8th, 2009 Structure says:

Let

$$p_1=b+c\:q_1=bc$$
$$p_2=a+c\:q_2=ac$$
$$p_3=a+b\:q_3=ab$$

as I suppose -c is the common root of the first and the second equations and so on.
Your relation becomes

$$(b+c)^2+(c+a)^2+(a+b)^2+4(bc+ca+ab)=2((b+c)(c+a)+(c+a)(a+b)+(a+b)(b+c))$$

and is a simple identity.

Back to top