[Toán 12] Định a để pt có nghiệm

N

nguyenbahiep1

[laTEX]a = \sqrt{x^2-x}+x-1 \\ \\ f(x) = \sqrt{x^2-x}+x-1 \\ \\ txd: x < 0 , x > 1 \\ \\ y' > 0 \Rightarrow x \in ( 1, +\infty ) \\ \\ y' < 0 \Rightarrow x \in ( -\infty , 0 ) \\ \\ \lim_{ x \to +\infty}f(x) = + \infty \\ \\ \lim_{ x \to -\infty}f(x) = -\frac{1}{2} \\ \\ f(0) = -1 \\ \\ f(1) = 0 [/laTEX]


vậy pt có nghiệm khi

[laTEX]a \in [ -1, -\frac{1}{2}) \cup [0, +\infty)[/laTEX]
 
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