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Q.
Let $a, b, c d \in R$ be such that $a^2+b^2+c^2+d^2=25$, then
Complex Numbers and Quadratic Equations
Solution:
$ \text { Given, } a ^2+ b ^2+ c ^2+ d ^2=25 $
$\text { As, } ( a - b )^2+( b - c )^2+( c - d )^2+( d - a )^2 \geq 0 $
$\Rightarrow 2\left( a ^2+ b ^2+ c ^2+ d ^2\right) \geq 2( ab + bc + cd + ad )$
$\Rightarrow ab + bc + cd + da \leq 25$