What will be the value of the following?\( \sqrt {6+\sqrt {6+\sqrt{6+ ………..}}}\)
What will be the value of the following?
निम्न का मान क्या होगा ?
\( \sqrt {6+\sqrt {6+\sqrt{6+ ………..}}}\)
Detailed Solution & Logic
Correct Answer:
3
मान लें:
$x=\sqrt{6+\sqrt{6+\sqrt{6+\cdots}}}$
तो अंदर का पूरा भाग फिर से $x$ है:
$x=\sqrt{6+x}$
Squaring:
$x^2=6+x$
$x^2-x-6=0$
$(x-3)(x+2)=0$
Square root होने के कारण $x$ धनात्मक होगा, इसलिए:
$x=3$
सही उत्तर: 3
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