Let a,b, and c be nonzero real numbers such that a+b+c=0. Simplify b2+c2−a21+a2+c2−b21+a2+b2−c21.
Solution — click to reveal
From the equation a+b+c=0,a=−b−c, so b2+c2−a21=b2+c2−(b+c)21=−2bc1=−2bc1.Similarly, a2+c2−b21=−2ac1anda2+b2−c21=−2ab1,so b2+c2−a21+a2+c2−b21+a2+b2−c21=−2bc1−2ac1−2ab1=−2abca+b+c=0.