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Solve x(x+2)^2(x-1)^5(2x-3)(x-3)^4geq0....

Solve `x(x+2)^2(x-1)^5(2x-3)(x-3)^4geq0.`

Text Solution

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`x(2^x-1)(3^x-9)(x-3)`
Here for x ,(x-1),(2x-3), exponents are odd hence , the sign of E changes while crossing x= 0 1, 3/2 Also for (x+2) n(x-3) exponents are even hence the sing of E does not changes while crossing x= -2 and x=3
Futher for x- 2 and x-3 all factors are positive .hence the sisgn of the expression starts with a positive sign from sign from the right hand side
The sign scheme of the expression is as follows.

Hence , for `E ge 0,` we have x in `[0,1] cup [ 3/2 , oo] `
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