CBSE BoardEnglish MediumSTD 10MathsQuadratic Equations1 Mark
MCQ
The value of $\sqrt{6+\sqrt{6+\sqrt{6+}}}...$ is:
A
$4$
✓
$3$
C
$-2$
D
$3.5$
✓
Answer
Correct option: B.
$3$
Let $\text{x}=\sqrt{6+\sqrt{6+\sqrt{6+}}}...$
$\Rightarrow\text{x}=\sqrt{6+\text{x}}$
$ \Rightarrow x^2=6+x $
$ \Rightarrow x^2-x-6=0 $
$ \Rightarrow x^2-3 x+2 x-6=0 $
$ \Rightarrow x(x-3)+2(x-3)=0 $
$ \Rightarrow(x-3)(x+2)=0$
Either $x-3=0$, then $x=3$ Or
$x+2=0$, then $x=-2$
Now if $x = 3$, then
$3=\sqrt{6+\sqrt{6+\sqrt{6+}}}...$
$=\sqrt{6+ 3}=\sqrt{9}$
$=3$
If $x = -2,$ then
$\Rightarrow\text{x}=\sqrt{6+\text{x}}$
$\Rightarrow-2=\sqrt{6-2}$
$\Rightarrow-2=\sqrt{4}$
$\Rightarrow-2\neq2$
Which is not possible $x = 3$ is correct.
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