Question

$\sqrt{72 + \sqrt{72 + \sqrt{72 + ...} } }$
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Answer 1

Step-by-step explanation:

$</p><p>let \: \\ x = \sqrt{72 + \sqrt{72 + \sqrt{72 + ...} } } </p><p>$

then,

$x = \sqrt{(72 + x)}$

Square both sides,

${x}^{2} = (72 + x)$

${x}^{2} - x - 72 = 0$

$x =(1 + \sqrt{1 + 288} ) \div 2 \: \: or \: \: (1 - \sqrt{1 + 288} ) \div 2$

$x = (1 + 17) \div 2 = 9 \\ or \\ (1 - 17) \div 2 = - 8$

ANS.