![radicals - Use the Cauchy-Schwarz Inequality to prove that $a^2+b^2+c^2 \ge ab+ac+bc $ for all positive $a,b,c$. - Mathematics Stack Exchange radicals - Use the Cauchy-Schwarz Inequality to prove that $a^2+b^2+c^2 \ge ab+ac+bc $ for all positive $a,b,c$. - Mathematics Stack Exchange](https://i.stack.imgur.com/UVS3U.png)
radicals - Use the Cauchy-Schwarz Inequality to prove that $a^2+b^2+c^2 \ge ab+ac+bc $ for all positive $a,b,c$. - Mathematics Stack Exchange
if the roots of the equation a(b c)x^2+b(c a)x+c(a b)=0 are equal and a,b,c>0, then prove that 2/b=1/a+1/c, i.e., a,b,c are in H.P.
![If a2+b2+c2=74 and ab+bc+ca= 61, find a+b+c - Maths - Indices and Logarithms - 14186571 | Meritnation.com If a2+b2+c2=74 and ab+bc+ca= 61, find a+b+c - Maths - Indices and Logarithms - 14186571 | Meritnation.com](https://s3mn.mnimgs.com/img/shared/content_ck_images/ck_103671dbaee1c784596e7114e3cb961d.png)
If a2+b2+c2=74 and ab+bc+ca= 61, find a+b+c - Maths - Indices and Logarithms - 14186571 | Meritnation.com
![If a2 + b2 + c2 ab - bc - ca = 0 , prove that a=b=c - Maths - Polynomials - 1243710 | Meritnation.com If a2 + b2 + c2 ab - bc - ca = 0 , prove that a=b=c - Maths - Polynomials - 1243710 | Meritnation.com](https://s3mn.mnimgs.com/img/shared/userimages/mn_images/image/a1(1762).png)