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Giải bài 17 trang 10 sách bài tập toán 10 - Cánh diều

Phát biểu mệnh đề đảo của mệnh đề trên. Mệnh đề đảo đúng hay sai?

🎐Tổng hợp đề thi học kì 2 lớp 10 tất cả các môn - Cánh diều

Toán - Văn - Anh - Lí - Hóa - Sinh - Sử - Địa...
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Đề bài

Cho phương trình \(a{x^2} + bx + c = 0\). a) Xét mệnh đề “Nếu \(a + b + c = 0\) thì phương trình \(a{x^2} + bx + c = 0\) có một nghiệm bằng 1”. Mệnh đề này đúng hay sai? b) Phát biểu mệnh đề đảo của mệnh đề trên. Mệnh đề đảo đúng hay sai? c) Nêu điều kiện cần vào đủ để phương trình \(a{x^2} + bx + c = 0\) có một nghiệm bằng 1.

Phương pháp giải - Xem chi tiết

Mệnh đề đảo của \(P \Rightarrow Q\) là \(Q \Rightarrow P\). Nếu \(P \Rightarrow Q\) và \(Q \Rightarrow P\) đều đúng thì ta có mệnh đề tương đương \(P \Leftrightarrow Q\), có thể phát biểu dạng: “Điều kiện cần vào đủ để có P là Q”.

Lời giải chi tiết

a) Mệnh đề này đúng.                          \(a + b + c = 0\) hay \(a{.1^2} + b.1 + c = 0\), do đó \(x = 1\) là nghiệm của phương trình \(a{x^2} + bx + c = 0\). b) Mệnh đề đảo: “Nếu phương trình \(a{x^2} + bx + c = 0\) có một nghiệm bằng 1 thì \(a + b + c = 0\)”. Mệnh đề đảo này đúng. c) Điều kiện cần và đủ để phương trình \(a{x^2} + bx + c = 0\) có một nghiệm bằng 1 là \(a + b + c = 0\).

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Ph/hs Tham Gia Nhóm Để Cập Nhật Điểm Thi, Điểm Chuẩn Miễn Phí

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