Question
The value of $√{72+√{72+√{72 +...}}}$ is
Answer: Option D
Answer: (d)x = $√{72+√{72+√{72 +...}}}$On squaring both sides,$x^2 = 72+√{72+√{72+√{72 +...}}}$$x^2$ = 72 + x$x^2$ - x - 72 = 0$x^2$ - 9x + 8x - 72 = 0x (x - 9) + 8 (x - 9) = 0(x + 8) (x - 9) = 0x = 9 because x ≠ - 8Using Rule 25$√{72+√{72+√{72 +...}}}$ = 9It is because 72 = 8×9 = n (n + 1)
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Answer: (d)x = $√{72+√{72+√{72 +...}}}$On squaring both sides,$x^2 = 72+√{72+√{72+√{72 +...}}}$$x^2$ = 72 + x$x^2$ - x - 72 = 0$x^2$ - 9x + 8x - 72 = 0x (x - 9) + 8 (x - 9) = 0(x + 8) (x - 9) = 0x = 9 because x ≠ - 8Using Rule 25$√{72+√{72+√{72 +...}}}$ = 9It is because 72 = 8×9 = n (n + 1)
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