PHP, 37 Bytes

Prints 1 for true and nothing for false

<?=($x=sqrt($q=2*$argn)^0)*$x+$x==$q;

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PHP, 30 Bytes

Prints 1 for true and nothing for false

<?=fmod(sqrt(8*$argn+1),2)==1;

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fmod

PHP, 37 Bytes

Prints 1 for true and nothing for false

<?=($x=sqrt($q=2*$argn)^0)*$x+$x==$q;

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PHP, 40 Bytes

Prints 1 for true and nothing for false

echo$argn*2==($x=sqrt(2*$argn)^0)*$x+$x;

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PHP, 37 Bytes

Prints 1 for true and nothing for false

<?=($x=sqrt($q=2*$argn)^0)*$x+$x==$q;

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