Toán 9 Giải hệ phương trình

[Vinh Tino (tông sư)]

[TẶNG BẠN] TRỌN BỘ Bí kíp học tốt 08 môn
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giải hệ phương trình sau

[tex]\left\{\begin{matrix} x+y=5 & & \\ x^{4}+y^{4}=97 & & \end{matrix}\right.[/tex]

 

[tyioit]

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[Sơn Nguyên 05]

Dùng hệ đối xứng loại 1" role="presentation" style="margin: 0px; padding: 0px; border: 0px; font-size: 13.696px; vertical-align: baseline; background: rgb(255, 255, 255); display: inline; line-height: normal; word-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; color: rgb(0, 0, 0); font-family: Arial, "Liberation Sans", "DejaVu Sans", sans-serif; position: relative;">11 làm
Pt 2 viết thành (x2+y2)2−2x2y2=97" role="presentation" style="margin: 0px; padding: 0px; border: 0px; font-size: 13.696px; vertical-align: baseline; background: transparent; display: inline; line-height: normal; word-spacing: normal; word-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; position: relative;">(x2+y2)2−2x2y2=97(x2+y2)2−2x2y2=97
⇔[(x+y)2−2xy]2−2x2y2=97" role="presentation" style="margin: 0px; padding: 0px; border: 0px; font-size: 13.696px; vertical-align: baseline; background: transparent; display: inline; line-height: normal; word-spacing: normal; word-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; position: relative;">⇔[(x+y)2−2xy]2−2x2y2=97⇔[(x+y)2−2xy]2−2x2y2=97

Thế x+y=5" role="presentation" style="margin: 0px; padding: 0px; border: 0px; font-size: 13.696px; vertical-align: baseline; background: transparent; display: inline; line-height: normal; word-spacing: normal; word-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; position: relative;">x+y=5x+y=5 vào ta được

(25−2xy)2−2(xy)2=97" role="presentation" style="margin: 0px; padding: 0px; border: 0px; font-size: 13.696px; vertical-align: baseline; background: transparent; display: inline; line-height: normal; word-spacing: normal; word-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; position: relative;">(25−2xy)2−2(xy)2=97(25−2xy)2−2(xy)2=97

⇔xy=6" role="presentation" style="margin: 0px; padding: 0px; border: 0px; font-size: 13.696px; vertical-align: baseline; background: transparent; display: inline; line-height: normal; word-spacing: normal; word-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; position: relative;">⇔xy=6⇔xy=6 hoặc xy=44" role="presentation" style="margin: 0px; padding: 0px; border: 0px; font-size: 13.696px; vertical-align: baseline; background: transparent; display: inline; line-height: normal; word-spacing: normal; word-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; position: relative;">xy=44xy=44
Ta có cặp x+y=5;&#xA0;xy=44" role="presentation" style="margin: 0px; padding: 0px; border: 0px; font-size: 13.696px; vertical-align: baseline; background: transparent; display: inline; line-height: normal; word-spacing: normal; word-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; position: relative;">x+y=5; xy=44x+y=5; xy=44 vô nghiệ vì S2&lt;4P" role="presentation" style="margin: 0px; padding: 0px; border: 0px; font-size: 13.696px; vertical-align: baseline; background: transparent; display: inline; line-height: normal; word-spacing: normal; word-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; position: relative;">S2<4PS2<4P
Cặp x+y=5;&#xA0;xy=6" role="presentation" style="margin: 0px; padding: 0px; border: 0px; font-size: 13.696px; vertical-align: baseline; background: transparent; display: inline; line-height: normal; word-spacing: normal; word-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; position: relative;">x+y=5; xy=6x+y=5; xy=6, ta có x;&#xA0;y" role="presentation" style="margin: 0px; padding: 0px; border: 0px; font-size: 13.696px; vertical-align: baseline; background: transparent; display: inline; line-height: normal; word-spacing: normal; word-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; position: relative;">x; yx; y là nghiệm pt t2&#x2212;5t+6=0" role="presentation" style="margin: 0px; padding: 0px; border: 0px; font-size: 13.696px; vertical-align: baseline; background: transparent; display: inline; line-height: normal; word-spacing: normal; word-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; position: relative;">t2−5t+6=0t2−5t+6=0
&#x21D4;t=2;&#xA0;t=3" role="presentation" style="margin: 0px; padding: 0px; border: 0px; font-size: 13.696px; vertical-align: baseline; background: transparent; display: inline; line-height: normal; word-spacing: normal; word-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; position: relative;">⇔t=2; t=3⇔t=2; t=3
Hệ có nghiệm (x;&#xA0;y)=(2;&#xA0;3);&#xA0;(3;&#xA0;2)" role="presentation" style="margin: 0px; padding: 0px; border: 0px; font-size: 13.696px; vertical-align: baseline; background: transparent; display: inline; line-height: normal; word-spacing: normal; word-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; position: relative;">(x; y)=(2; 3); (3; 2)

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[tyioit]

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