We know that the square of any number is greater than or equal to zero ;
So if have a number like x :
[tex]( {x})^{2} \geqslant 0[/tex]
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Now we have a number which is
( a - b ) ;
So we have :
[tex]( {a - b})^{2} \geqslant 0 [/tex]
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Reminder :
[tex]( {a - b})^{2} = {a}^{2} - 2ab + {b}^{2} [/tex]
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So we have :
[tex] {a}^{2} - 2ab + {b}^{2} \geqslant 0 [/tex]
Both sides plus 2ab :
[tex] {a}^{2} + {b}^{2} \geqslant 2ab [/tex]
Divided both sides by 2 :
[tex] \frac{ {a}^{2} + {b}^{2} }{2} \geqslant ab \\ [/tex]
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And we're done.
Thanks for watching buddy good luck.
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