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Giải bài 5 trang 23 vở thực hành Toán 9 tập 2

Tìm hai số u và v, biết: a) (u + v = 20,uv = 99); b) (u + v = 2,uv = 15).

Tổng hợp Đề thi vào 10 có đáp án và lời giải

Toán - Văn - Anh
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Đề bài

Tìm hai số u và v, biết: a) \(u + v = 20,uv = 99\); b) \(u + v = 2,uv = 15\).

Phương pháp giải - Xem chi tiết

+ Hai số cần tìm là hai nghiệm của phương trình \({x^2} - Sx + P = 0\) (điều kiện \({S^2} - 4P \ge 0\)). + Tính nghiệm của phương trình dựa vào công thức nghiệm (hoặc công thức nghiệm thu gọn).

Lời giải chi tiết

a) Hai số cần tìm là hai nghiệm của phương trình \({x^2} - 20x + 99 = 0\) Ta có: \(\Delta  = {\left( { - 20} \right)^2} - 4.1.99 = 4 > 0,\sqrt \Delta = 2\) Suy ra phương trình có hai nghiệm: \({x_1} = \frac{{20 + 2}}{2} = 11;{x_2} = \frac{{20 - 2}}{2} = 9\).

Vậy \(\left( {u;v} \right) = \left( {11;9} \right)\) hoặc \(\left( {u;v} \right) = \left( {9;11} \right)\).

b) Hai số cần tìm là hai nghiệm của phương trình \({x^2} - 2x + 15 = 0\). Ta có: \(\Delta  = {\left( { - 2} \right)^2} - 4.1.15 =  - 56 < 0\) Suy ra phương trình đã cho vô nghiệm. Vậy không tồn tại hai số u, v thỏa mãn điều kiện đã cho.

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