Question
$√{12+√{12+√{12 +...}}}$ is equal to
Answer: Option B
Answer: (b)Let x = $√{12+√{12+√{12 +...}}}$On squaring both sides,$x^2 =12+√{12+√{12+√{12 +...}}}$$x^2$ = 12 + x$x^2$ - x - 12 = 0$x^2$ - 4x + 3x - 12 = 0x (x - 4) + 3 (x - 4) = 0(x - 4) (x + 3) = 0x = 4, - 3The given expression is positive.x = 4 Using Rule 25If $√{x+√{x+√{x +...∞}}}$ where, x=n(n + 1)then $√{x+√{x+√{x +...∞}}}$ = (n + 1)
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Answer: (b)Let x = $√{12+√{12+√{12 +...}}}$On squaring both sides,$x^2 =12+√{12+√{12+√{12 +...}}}$$x^2$ = 12 + x$x^2$ - x - 12 = 0$x^2$ - 4x + 3x - 12 = 0x (x - 4) + 3 (x - 4) = 0(x - 4) (x + 3) = 0x = 4, - 3The given expression is positive.x = 4 Using Rule 25If $√{x+√{x+√{x +...∞}}}$ where, x=n(n + 1)then $√{x+√{x+√{x +...∞}}}$ = (n + 1)
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