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Debashis Roy

· started a discussion

· 1 Months ago

The question is wrong.

Question:
The value of \(\sqrt[]{6+\sqrt[]{6}+\sqrt[]{6}+...}\)    is equal to:
Options:
A) 2
B) 3
C) \(\sqrt[]{6}\)
D) 6
Solution:
Ans: (b) let \(y=\sqrt[]{6+\sqrt[]{6}+\sqrt[]{6}+...\infty}\)

\(y=\sqrt[]{6+y}\)

squaring 

y2 = 6 + y

y2 - y - 6 = 0

(y-3) (y+2) = 0

\(\therefore\) y = 3, or y = -2

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