Đáp án: x^3+3y^2+2xy−18(x+y)+73=0 tìm nghiệm nguyên - Xin hay nhất ạ

Sửa lại đề là x^2 nhé k phải x^3 x^2+3y^2+2xy-18(x+y)+73=0 <=> x^2+2xy+y^2 -18(x+y) + 73+8+2y^2= 8 <=> (x+y)^2-18(x+y)+81=8-2y^2 <=> (x+y-9)^2=8-2y^2 Do (x+y-9)^2 ≥ 0 với mọi x ⇒8-2y^2 ≥ 0 ⇒ 2y^2 ≤ 8 ⇔ y^2 ≤ 4 ⇔ -2 ≤ y ≤ 2 mà y ∈ Z ⇒ y ∈ (-2;-1;0;1;2) Với y=0 ==> (x+y-9)^2=8 (Loại) Với y = 1 ==> (x+y-9)^2=6 (Loại) Với y = -1 ==> (x+y-9)^2=6 (Loại) Với y = 2 ==> (x+y-9)^2=0 ⇒ x = 7 Với y = -2 ⇒(x+y-9)^2=0 ⇒ x = -11 (x;y)=(7;2);(-11;-2) Vote giúp mình 5 sao nhé

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x^3+3y^2+2xy−18(x+y)+73=0 tìm nghiệm nguyên

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phammanhcuong07

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Sửa lại đề là x^2 nhé k phải x^3

x^2+3y^2+2xy-18(x+y)+73=0

<=> x^2+2xy+y^2 -18(x+y) + 73+8+2y^2= 8

<=> (x+y)^2-18(x+y)+81=8-2y^2

<=> (x+y-9)^2=8-2y^2

Do (x+y-9)^2 ≥ 0 với mọi x

⇒8-2y^2 ≥ 0

⇒ 2y^2 ≤ 8

⇔ y^2 ≤ 4

⇔ -2 ≤ y ≤ 2

mà y $\in$

$\in$ $\in$

$\in$

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