February 23rd, 2019, 05:57 AM  #1 
Senior Member Joined: Dec 2015 From: somewhere Posts: 511 Thanks: 79  Need explanation
Just give the hint . (1) If $\displaystyle a+b+c=0 \; $ and $\displaystyle a\neq b \neq c\; $ a,b,c real numbers . Show that $\displaystyle \frac{a^2 }{bc +2a^2 } +\frac{b^2 }{ac+2b^2 } +\frac{c^2 }{ ab+2c^2 }=1$ . (2) Factorize the polynomial : $\displaystyle x^7 +x^5 +1$ . 
February 23rd, 2019, 09:52 AM  #2 
Global Moderator Joined: Dec 2006 Posts: 20,628 Thanks: 2077 
(1) Replace $a$ with $(b + c)$ throughout the lefthand side of the equation to be proved. (2) Try to find a quadratic factor. 

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