Question 4

Determine the value of 'Z' $$Z=\sqrt{20+\sqrt{20+\sqrt{20+\sqrt{20+.....}}}}$$

Solution

Expression : $$Z=\sqrt{20+\sqrt{20+\sqrt{20+\sqrt{20+.....}}}}$$

=> $$Z=\sqrt{20+Z}$$

Squaring both sides, we get :

=> $$Z^2=20+Z$$

=> $$Z^2-Z-20=0$$

=> $$Z^2+4Z-5Z-20=0$$

=> $$Z(Z+4)-5(Z+4)=0$$

=> $$(Z+4)(Z-5)=0$$

=> $$Z=-4,5$$

But $$Z$$ cannot be negative, => $$Z=5$$

=> Ans - (B)

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