Question

$\sqrt{12 + \sqrt{12 + \sqrt{12 + ............. \infty } } }$
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Answer 1

$<b><marquee>Answer</marquee></b>$

$Let \: x=\sqrt{12+\sqrt{12+\cdots}}\\</p><p>\implies x=\sqrt{12+x}\\</p><p>x^2=12+x\\</p><p>x^2-x-12=0\\</p><p>(x-4)(x+3)=0\\</p><p>\implies x=4 \: or\: x=-3\\</p><p>\text{Since radical is non-negative,}\\</p><p>\boxed {x=4}$