Question

The value of $\sqrt{42+\sqrt{42+\sqrt{42+....\infty }}}$ is

• A. $7$
• B. $6$
• C. $5$
• D. $3$

Answer 1

The correct option is A $7$

$\sqrt{42+\sqrt{42+....\infty }}=x$ (say)

Squaring

$42+\sqrt{42+\sqrt{42+....\infty }}=x^2\Rightarrow x^2=42+x$

$\Rightarrow (x-7)(x+6)=0\Rightarrow x=7,-6$ As $x>0\Rightarrow x=7$