Search any question & find its solution
Question:
Answered & Verified by Expert
The value of $\sqrt{42+\sqrt{42+\sqrt{42+\ldots \ldots .}}}$ is equal
Options:
Solution:
1907 Upvotes
Verified Answer
The correct answer is:
$7$
Let $y=\sqrt{42+\sqrt{42+\sqrt{42+\ldots}}}$
$$
\Rightarrow \quad y=\sqrt{42+y}
$$
On squaring both sides, we get
$$
\begin{aligned}
& y^2=42+y \\
& \Rightarrow \quad y^2-y-42=0 \\
&
\end{aligned}
$$
$$
\begin{array}{rlrl}
\Rightarrow & & (y-7)(y+6) & =0 \\
\Rightarrow & y =7,-6
\end{array}
$$
Since, $y=-6$ is not satisfied the given equation.
$\therefore$ The required solution is $y=7$.
$$
\Rightarrow \quad y=\sqrt{42+y}
$$
On squaring both sides, we get
$$
\begin{aligned}
& y^2=42+y \\
& \Rightarrow \quad y^2-y-42=0 \\
&
\end{aligned}
$$
$$
\begin{array}{rlrl}
\Rightarrow & & (y-7)(y+6) & =0 \\
\Rightarrow & y =7,-6
\end{array}
$$
Since, $y=-6$ is not satisfied the given equation.
$\therefore$ The required solution is $y=7$.
Looking for more such questions to practice?
Download the MARKS App - The ultimate prep app for IIT JEE & NEET with chapter-wise PYQs, revision notes, formula sheets, custom tests & much more.