Question

Find the value of $\sqrt{30+\sqrt{30+\sqrt{30+\cdots \infty }}}$.

• A. 6
• B. -5
• C. Either (a) or (b)
• D. Neither(a) nor (b)

Answer 1

Answer: (A)

$x=\sqrt{30+x}$
Squaring on both sides, we get $x^2=30+x$
$x^2-x-30=0$
$(x-6)(x+5)=0$
$x=6\text{ or }-5$
But $x$ must be positive.
$\therefore x=6.$