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huyhoangnguyen094
2 năm trước
a, Tìm đa thức bậc hai biết f(x)- f(x-1) =x . Từ đó áp dụng tính tổng `S = 1 + 2 + 3 + ............. + n` b, Cho `(2bz - 3cy)/a = (3cx - az)/2b = (ay - 2bx)/3c` . Chứng minh `x/a = y/(2b) = z/(3c)`
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Cau hoi: Xét đúng (sai) mệnh đề và phủ định mệnh đề sau : \(\forall x \in \mathbb{R}\) \({x^4} - {x^2} + 1 = \left( {{x^2} + \sqrt 3 x + 1} \right)\left( {{x^2} - \sqrt 3 x + 1} \right)\) A. Mệnh đề \(\forall x \in \mathbb{R},\,\,{x^4} - {x^2} + 1 = \left( {{x^2} + \sqrt 3 x + 1} \right)\left( {{x^2} - \sqrt 3 x + 1} \right)\) đúng Mệnh đề phủ định là \(\exists x \in \mathbb{R},\,\,{x^4} - {x^2} + 1 \ne \left( {{x^2} + \sqrt 3 x + 1} \right)\left( {{x^2} - \sqrt 3 x + 1} \right)\). B. Mệnh đề \(\forall x \in \mathbb{R},\,\,{x^4} - {x^2} + 1 = \left( {{x^2} + \sqrt 3 x + 1} \right)\left( {{x^2} - \sqrt 3 x + 1} \right)\) đúng Mệnh đề phủ định là \(x \in \mathbb{R},\,\,{x^4} - {x^2} + 1 \ne \left( {{x^2} + \sqrt 3 x + 1} \right)\left( {{x^2} - \sqrt 3 x + 1} \right)\). C. Mệnh đề \(\forall x \in \mathbb{R},\,\,{x^4} - {x^2} + 1 = \left( {{x^2} + \sqrt 3 x + 1} \right)\left( {{x^2} - \sqrt 3 x + 1} \right)\) sai Mệnh đề phủ định là \(\exists x \in \mathbb{R},\,\,{x^4} - {x^2} + 1 \ne \left( {{x^2} + \sqrt 3 x + 1} \right)\left( {{x^2} - \sqrt 3 x + 1} \right)\). D. Mệnh đề \(\forall x \in \mathbb{R},\,\,{x^4} - {x^2} + 1 = \left( {{x^2} + \sqrt 3 x + 1} \right)\left( {{x^2} - \sqrt 3 x + 1} \right)\) sai Mệnh đề phủ định là \(x \in \mathbb{R},\,\,{x^4} - {x^2} + 1 \ne \left( {{x^2} + \sqrt 3 x + 1} \right)\left( {{x^2} - \sqrt 3 x + 1} \right)\)

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