Question

# Find the value y=3√6+3√6+3√63√6+....∞

A
2
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B
4
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C
6
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D
12
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Solution

## The correct option is A 2This is the given equation and we have to find the value of y. See the equation properly,y=3√6+3√6+3√63√6+.....∞ Let assume the term x which is,y=3√6+3√6+3√6∗xWe have,x=3√6+3√6+3√6+3√6+.....∞ If we see properly the expression they are getting repeated. So we can write it as,x=3√6+xOn cubing both sides we get,or,x3=6+xor,x3−x−6=0On solving this cubic equation we get,(x−2)(x2+2x+3)=0Therefore we get the value of x is 2.Now putting the value of x in original equation we get,y=3√6+3√6+3√6×2 or,y=3√6+3√6+3√6×2 or,y=3√6+3√6+3√12This is the obtained answer.

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