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Giải bài 6 trang 34 vở thực hành Toán 8

a) Cho \(a + b = 7\) và \(ab = 12\). Tính \({a^3} + {b^3}.\)

ಞTổng hợp đề thi học kì 2 lớp 8 tất cả các môn - Kết nối tri thức

Toán - Văn - Anh - Khoa học tự nhiên
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Đề bài

🃏a) Cho \(a + b = 7\) và \(ab = 12\). Tính \({a^3} + {b^3}.\)

🍌b) Cho \(a-b = 1\) và \(ab = 12\). Tính \({a^3} - {b^3}.\)

Phương pháp giải - Xem chi tiết

🐠a) Sử dụng hằng đẳng thức tổng hai lập phương: \({a^3} + {b^3} = (a + b)\left( {{a^2} - ab + {b^2}} \right)\)

✃b) Sử dụng hằng đẳng thức hiệu hai lập phương: \({a^3} - {b^3} = \left( {a - b} \right)\left( {{a^2} + ab + {b^2}} \right)\)

Lời giải chi tiết

♎a) Ta có \({a^3} + {b^3} = {(a + b)^3} - 3ab(a + b) = {7^3} - 3.12.7 = 91.\)

💙b) Ta có \({a^3} - {b^3} = {(a - b)^3} + 3ab(a - b) = {1^3} + 3.12.1 = 37.\)

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