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Question
Find the value y=3√6+3√6+3√63√6+....∞
Find the value y=3√6+3√6+3√63√6+....∞
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Solution
The correct option is A 2
This 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∗x
We 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+x
On cubing both sides we get,
or,x3=6+x
or,x3−x−6=0
On solving this cubic equation we get,
(x−2)(x2+2x+3)=0
Therefore 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√12
This is the obtained answer.
This 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∗x
We 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+x
On cubing both sides we get,
or,x3=6+x
or,x3−x−6=0
On solving this cubic equation we get,
(x−2)(x2+2x+3)=0
Therefore 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√12
This is the obtained answer.
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