Radical Infinity

Algebra Level 2

If 3 = x + x + x + . . . 3= \sqrt{x+\sqrt{x+\sqrt{x+...}}} , what is x = ? x=?


The answer is 6.

Yellow Tomato by Yellow Tomato , 17, USA

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2 solutions

Rohit Udaiwal
Oct 22, 2015

3 = x + x + x + . . . 9 = x + 3 x = 6 3= \sqrt{x+\sqrt{x+\sqrt{x+...}}}\\ 9=x+3 \\ \boxed{x=6}

4 Helpful 0 Interesting 0 Brilliant 0 Confused
Sangamesh Rk
Oct 22, 2015

IF 3=√x+√x.......----1

Squaring both sides we get

9=x+√x+√x....

9-x=√x+√x.....------2

1=2

9-x=3

x=6

2 Helpful 0 Interesting 0 Brilliant 0 Confused

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