12)
|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?)
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??
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5 Answers
1
341I. 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