Câu trả lời hay nhất: Giai cau a)
x³ - y³ = xy + 8
<=> (x - y)³ + 3xy(x - y) - xy = 8
<=> (x - y)³ + xy(3x - 3y - 1) = 8
<=> (3x - 3y)³ + 27xy(3x - 3y - 1) = 216
<=> (3x - 3y)³ - 1 + 27xy(3x - 3y - 1) = 215
<=> (3x - 3y - 1)[(3x - 3y)² + (3x - 3y) + 1] + 27xy(3x - 3y - 1) = 215
<=> (3x - 3y - 1)[(3x - 3y)² + (3x - 3y) + 1 + 27xy] = 215
<=> (3x - 3y - 1)(9x² + 9y² - 9xy + 3x - 3y + 1) = 215 = 5.43 = 43.5 = (- 5)(- 43) = (- 43)(- 5)
{ 3x - 3y - 1 = 5 (1)
{ 9x² + 9y² - 9xy + 3x - 3y + 1 = 43 (2)
Tu (1) => y = x - 2 thay vao (2) khai trien rut gon co x(x - 2) = 0
=> x = 0; x = 2 => y = - 2; y = 0
Truong hop nay he co 2 nghiem nguyen (x;y) = (0; - 2) va (2; 0)
{ 3x - 3y - 1 = 43 (3)
{ 9x² + 9y² - 9xy + 3x - 3y + 1 = 5 (4)
{ 3x - 3y - 1 = - 5 (5)
{ 9x² + 9y² - 9xy + 3x - 3y + 1 = - 43 (6)
{ 3x - 3y - 1 = - 43 (7)
{ 9x² + 9y² - 9xy + 3x - 3y + 1 = - 5 (8)
Ban tu giai tiep 3 he sau ( chu y chon nghiem nguyen ) roi ket luan
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Ban xem vi du sau: Giai pt nghiem nguyen
2x² - 2x - 2y² = - 3
<=> 4x² - 4x - 4y² + 1 = - 5
<=> (2x + 2y - 1)(2x - 2y - 1) = - 5 = - 1.5 = 1.(- 5) = 5.( -1 ) = (- 5).1
{ 2x + 2y - 1 = - 1
{ 2x - 2y - 1 = 5
=> x = 3/2 ; y = - 3/2 ( loai )
{ 2x + 2y - 1 = 1
{ 2x - 2y - 1 = - 5
=> x = - 1/2 ; y = 3/2 ( loai )
{ 2x + 2y - 1 = 5
{ 2x - 2y - 1 = - 1
=> x = 3/2 ; y = 3/2 ( loai )
{ 2x + 2y - 1 = - 5
{ 2x - 2y - 1 = 1
=> x = - 1/2 ; y = - 3/2 ( loai)
KL : Pt khong co nghiem nguyen
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Voi dang phuong trinh nghiem nguyen bac 2 nay minh bay ban mot thu thuat phan h thanh nhan tu de lam, bat ky bai nao cung giai quyet duoc
Vi du : Xet pt : 2x² - 2x + 3 = 2y²
Buoc 1 : Chuyen ta ca cac hang tu co chua an sang mot ve
2x² - 2x - 2y² = - 3
Them vao 2 ve mot so a nao do
2x² - 2x - 2y² + a = a - 3
Xem ve trai la pt bac 2 an so x; tham so y can phan h thanh nhan tu. Muon vay delta phai la so chinh phuong
= 1 - 2(- 2y² + a) = 4y² + 1 - 2a
De la so chinhs phuong chon a = 1/2 => = 4y²
Khi do tam thuc ve trai co 2 nghiem : x = (1 - 2y)/2; x = (1 + 2y)/2
=> x + y - 1/2 = 0 va x - y - 1/2 = 0
Vay tam thuc co the phan h thanh : (x + y - 1/2)(x - y - 1/2) = - 5/2
hay (2x + 2y - 1)(2x - 2y - 1) = - 5
có đúng ko bn
