HD Online Player (Jhoom Barabar Jhoom Movie Hd Downloa) VERIFIED
HD Online Player (Jhoom Barabar Jhoom Movie Hd Downloa)
HD Online Player (Jhoom Barabar Jhoom movie hd downloa)
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I have to show the idea that the average of the square of the numbers is the square of the average, but i dont know how to prove it
Hi so i have to show the idea that the average of the square of the numbers is the square of the average, but i don’t know how to prove it. So could someone please explain to me how to do it.
A:
If $x_1,…,x_n$ are nonnegative, then $$\left(\frac1n\sum_{i=1}^n x_i\right)^2=\frac1n\sum_{i=1}^nx_i^2 \leq\frac1n\sum_{i=1}^nx_i^2\cdot n=n\frac1n\sum_{i=1}^nx_i^2$$
where the first inequality is obvious, so you just need to prove that $$n\frac1n\sum_{i=1}^nx_i^2\leq\frac1n\sum_{i=1}^nx_i^2\cdot n=\left(\frac1n\sum_{i=1}^nx_i\right)^2$$which it is because $$n\frac1n\sum_{i=1}^nx_i^2\leq n\frac1n\sum_{i=1}^nx_i \leq \left(\frac1n\sum_{i=1}^nx_i\right)^2$$
A:
If $a,b,c,d>0$ then we can write $$a+b+c+d=ab+ac+ad+bc+bd+cd$$
$$ = (a+b+c+d)^2$$
$$ = (ab+ac+bd+ad+bc+cd+ac+bd+cd)^2$$
$$= (ab+ac+bc+bd)^2 + (ad+ac+bd+cd)^2 +
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