Question
The value of the expression $√{6+√{6+√{6 +...+upto∞}}}$ is
Answer: Option B
Answer: (b)Let, x = $√{6+√{6+√{6 +...∞}}}$On squaring,$x^2 = 6 + √{6+√{6+√{6 +...∞}}}$$x^2$ = 6 + x$x^2$ - x - 6 = 0$x^2$ - 3x + 2x - 6 = 0x (x - 3) + 2 (x - 3) = 0(x + 2) (x - 3) = 0x = 3 because x ≠ - 2Using Rule 25$√{6+√{6+√{6 +...}}}$ = 3It is because, 6 = 2 × 3 =n (n+1)
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Answer: (b)Let, x = $√{6+√{6+√{6 +...∞}}}$On squaring,$x^2 = 6 + √{6+√{6+√{6 +...∞}}}$$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 ≠ - 2Using Rule 25$√{6+√{6+√{6 +...}}}$ = 3It is because, 6 = 2 × 3 =n (n+1)
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