Question 3
If $$x=\sqrt{15\sqrt{15\sqrt{15\sqrt{15\sqrt{15....\infty}}}}}$$ and x>0, then find the value of $$x^2+4$$
Solution
Expression : $$x=\sqrt{15\sqrt{15\sqrt{15\sqrt{15\sqrt{15....\infty}}}}}$$
=> $$x=\sqrt{15x}$$
Squaring both sides, we get :
=> $$x^2=15x$$
=> $$x=15$$
To find : $$x^2+4$$
= $$(15)^2+4=225+4=229$$
=> Ans - (D)
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