Question
$√{2+√{2+√{2 +...}}}$ is equal to
Answer: Option A
Answer: (a)Let x = $√{2+√{2+√{2 +...}}}$On squaring both sides$x^2 = 2+√{2+√{2+√{2 +...}}}$$x^2$ = 2 + x$x^2$ - x - 2 = 0$x^2$ - 2x + x - 2 = 0x (x - 2) + 1 (x - 2) = 0(x - 2) (x + 1) = 0x = 2 or - 1But sum of positive numbers can't be negative.x = 2
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Answer: (a)Let x = $√{2+√{2+√{2 +...}}}$On squaring both sides$x^2 = 2+√{2+√{2+√{2 +...}}}$$x^2$ = 2 + x$x^2$ - x - 2 = 0$x^2$ - 2x + x - 2 = 0x (x - 2) + 1 (x - 2) = 0(x - 2) (x + 1) = 0x = 2 or - 1But sum of positive numbers can't be negative.x = 2
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