Question
$√{6+√{6+√{6 +...}}}$ is equal to
Answer: Option D
Answer: (d) Let x = $√{6+√{6+√{6 +...}}}$Squaring on both sides,$x^2 = 6+√{6+√{6+√{6 +...}}}$$x^2$ = 6 + x$x^2$ - x - 6 = 0$x^2$ - 3x + 2x - 6 = 0x (x - 3) + 2 (x - 3) = 0(x + 2) (x - 3) = 0x = 3 because x ≠ - 2$√{6+√{6+√{6 +...}}}$ = 3It is because6 = 2 × 3 = n (n + 1)
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Answer: (d) Let x = $√{6+√{6+√{6 +...}}}$Squaring on both sides,$x^2 = 6+√{6+√{6+√{6 +...}}}$$x^2$ = 6 + x$x^2$ - x - 6 = 0$x^2$ - 3x + 2x - 6 = 0x (x - 3) + 2 (x - 3) = 0(x + 2) (x - 3) = 0x = 3 because x ≠ - 2$√{6+√{6+√{6 +...}}}$ = 3It is because6 = 2 × 3 = n (n + 1)
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