Toán tìm x,y ∈ Z thỏa mãn : 2$y^{2}$x+x+y+1 = $x^{2}$ + 2$y^{2}$ + xy 16/09/2021 By Kennedy tìm x,y ∈ Z thỏa mãn : 2$y^{2}$x+x+y+1 = $x^{2}$ + 2$y^{2}$ + xy
Đáp án: Giải thích các bước giải: $2xy² + x + y + 1 = x² + 2y² + xy$ $⇔ 2xy² – 2y² – x² + x – xy + y = – 1$ $⇔2y²(x – 1) – x(x – 1) – y(x – 1) = – 1$ $⇔(x – 1)(2y² – x – y) = – 1$ @ $\left \{ {{x – 1 = – 1} \atop {2y² – x – y = 1}} \right. ⇔ \left \{ {{x = 0} \atop {2y² – y – 1 = 0}} \right.$ $⇔ \left \{ {{x = 0} \atop {(y – 1)(2y + 1) = 0}} \right.⇔ \left \{ {{x = 0} \atop {y = 1}} \right.$ @ $\left \{ {{x – 1 = 1} \atop {2y² – x – y = – 1}} \right. ⇔ \left \{ {{x = 2} \atop {2y² – y – 1 = 0}} \right.$ $⇔ \left \{ {{x = 2} \atop {(y – 1)(2y + 1) = 0}} \right.⇔ \left \{ {{x = 2} \atop {y = 1}} \right.$ Trả lời
Đáp án:
Giải thích các bước giải:
$2xy² + x + y + 1 = x² + 2y² + xy$
$⇔ 2xy² – 2y² – x² + x – xy + y = – 1$
$⇔2y²(x – 1) – x(x – 1) – y(x – 1) = – 1$
$⇔(x – 1)(2y² – x – y) = – 1$
@ $\left \{ {{x – 1 = – 1} \atop {2y² – x – y = 1}} \right. ⇔ \left \{ {{x = 0} \atop {2y² – y – 1 = 0}} \right.$
$⇔ \left \{ {{x = 0} \atop {(y – 1)(2y + 1) = 0}} \right.⇔ \left \{ {{x = 0} \atop {y = 1}} \right.$
@ $\left \{ {{x – 1 = 1} \atop {2y² – x – y = – 1}} \right. ⇔ \left \{ {{x = 2} \atop {2y² – y – 1 = 0}} \right.$
$⇔ \left \{ {{x = 2} \atop {(y – 1)(2y + 1) = 0}} \right.⇔ \left \{ {{x = 2} \atop {y = 1}} \right.$