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Q.
Find the value of $\sqrt{30+\sqrt{30+\sqrt{30+\cdots \infty}}}$.
Quadratic Equations
Solution:
$x=\sqrt{30+x}$
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.
$\therefore x=6 .$