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find real roots of equation

\fn_cs \sqrt{x+2\sqrt{x+2\sqrt{x+........+2\sqrt{x+2\sqrt{3x}}}}} =x

\fn_cs \left ( \textbf{n radical signs} \right )

1) tell full solution wid explanation

2) what is radical signs??

#Mathematics #Algebra

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5 Answers

1

à¤œà¤¯ ·2010-06-29 01:52:00

2)

|x-1| +|7-x|+ 2|x-2|= 4

how to find intervals where expressions x-1 , 7-x , x-2 are of constant signs ??

and constant signs ( what does this mean?)

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à¤œà¤¯ ·2010-06-29 01:53:31

also draw the graphs and explain...

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341

Hari Shankar ·2010-06-29 08:01:31

I. 2) radical sign here refers to the square root signs, in general to nth root

1) x=3 is obviously a solution. Else

(a) x>3.

Then \sqrt{3x}<x \Rightarrow \sqrt{x + 2 \sqrt{3x}}<x

Successive use of this (starting from the right) gives you LHS<x

(b)x<3

Then \sqrt{3x}>x \Rightarrow \sqrt{x + 2 \sqrt{3x}}>x

Following the same procedure as above we get LHS>x

Thus x=3 is the unique solution

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341

Hari Shankar ·2010-06-29 08:02:38

Hint for 2: Triangle inequality

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à¤œà¤¯ ·2010-06-29 09:24:16

thank u sir .....

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Your Answer

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