Find the value of sqrt{30+sqrt{30+sqrt{30+cdo | vedclass

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(C) Let $x = \sqrt{30+\sqrt{30+\sqrt{30+\cdots}}}$.On squaring both sides,we get:$x^{2} = 30 + \sqrt{30+\sqrt{30+\sqrt{30+\cdots}}}$Since the expressi

Vedclass · Accepted Answer

$6$

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(C) Let $x = \sqrt{30+\sqrt{30+\sqrt{30+\cdots}}}$.On squaring both sides,we get:$x^{2} = 30 + \sqrt{30+\sqrt{30+\sqrt{30+\cdots}}}$Since the expression inside the square root is the same as $x$,we can write:$x^{2} = 30 + x$Rearranging the terms to form a quadratic equation:$x^{2} - x - 30 = 0$Factoring the quadratic equation:$x^{2} - 6x + 5x - 30 = 0$$x(x - 6) + 5(x - 6) = 0$$(x - 6)(x + 5) = 0$This gives $x = 6$ or $x = -5$.Since the value of the square root must be positive,we discard $x = -5$.Therefore,$x = 6$.

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

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