Question
Find the value of $√{30+√{30+√{30+...}}}$
Answer: Option A
Answer: (a)Let x = $√{30+√{30+√{30+...}}}$On squaring both sides,$x^2 = 30+√{30+√{30+√{30+...}}}$$x^2$ = 30 + x$x^2$ - x - 30 = 0$x^2$ - 6x + 5x - 30 = 0x (x - 6) + 5 (x - 6) = 0(x - 6) (x + 5) = 0x = 6 because x ≠ - 5Using Rule 25$√{30+√{30+√{30+...}}}$ = 6It is because30 = 5 × 6 = n (n +1)
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Answer: (a)Let x = $√{30+√{30+√{30+...}}}$On squaring both sides,$x^2 = 30+√{30+√{30+√{30+...}}}$$x^2$ = 30 + x$x^2$ - x - 30 = 0$x^2$ - 6x + 5x - 30 = 0x (x - 6) + 5 (x - 6) = 0(x - 6) (x + 5) = 0x = 6 because x ≠ - 5Using Rule 25$√{30+√{30+√{30+...}}}$ = 6It is because30 = 5 × 6 = n (n +1)
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