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Tìm x trực thuộc Z biết 2x + một là ước 3x – 2Sẽ vote 5 sao, thả tim và chọn hay tuyệt nhất ạ. Giải đáp mình phương pháp giải cụ thể với.
Tìm x trực thuộc Z biết 2x + 1 là ước 3x – 2Sẽ vote 5 sao, thả tim và chọn hay độc nhất vô nhị ạ. Gợi ý mình giải pháp giải chi tiết với.
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Đáp án:
Giải thích quá trình giải:
(2x+1) là cầu của (3x-2) yêu cầu ta có:
(eginarraylleft( 3x – 2 ight) vdots left( 2x + 1 ight)\Leftrightarrow 2left( 3x – 2 ight) vdots left( 2x + 1 ight)\Leftrightarrow left( 6x – 4 ight) vdots left( 2x + 1 ight)\Leftrightarrow left< 3left( 2x + 1 ight) – 7 ight> vdots left( 2x + 1 ight)\3left( 2x + 1 ight) vdots left( 2x + 1 ight) Rightarrow 7 vdots left( 2x + 1 ight)\Rightarrow 2x + 1 in left – 7;,, – 1;,,1;,,7 ight\\Rightarrow 2x in left – 8;,, – 2;,,0;,,6 ight\\Rightarrow x in left – 4;,, – 1;,,0;,,3 ight\endarray)
Thử lại ta thấy các giá trị bên trên của x phần lớn thỏa mãn.
Vậy (x in left – 4;,, – 1;,,0;,,3 ight\)
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(2x+1) là mong của (3x-2) cần ta có:
(3x−2)⋮(2x+1)⇔2(3x−2)⋮(2x+1)⇔(6x−4)⋮(2x+1)⇔<3(2x+1)−7>⋮(2x+1)3(2x+1)⋮(2x+1)⇒7⋮(2x+1)⇒2x+1∈−7;−1;1;7⇒2x∈−8;−2;0;6⇒x∈−4;−1;0;3" role="presentation" style="margin: 0px; padding: 1px 0px; display: inline-block; line-height: 0; text-indent: 0px; text-align: left; text-transform: none; font-style: normal; font-weight: normal; font-size: 18.15px; letter-spacing: normal; overflow-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; position: relative;" tabindex="0">(3x−2)⋮(2x+1)
(3x−2)⋮(2x+1)⇔2(3x−2)⋮(2x+1)⇔(6x−4)⋮(2x+1)⇔<3(2x+1)−7>⋮(2x+1)3(2x+1)⋮(2x+1)⇒7⋮(2x+1)⇒2x+1∈−7;−1;1;7⇒2x∈−8;−2;0;6⇒x∈−4;−1;0;3" role="presentation" style="margin: 0px; padding: 1px 0px; display: inline-block; line-height: 0; text-indent: 0px; text-align: left; text-transform: none; font-style: normal; font-weight: normal; font-size: 18.15px; letter-spacing: normal; overflow-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; position: relative;" tabindex="0">⇔2(3x−2)⋮(2x+1)
(3x−2)⋮(2x+1)⇔2(3x−2)⋮(2x+1)⇔(6x−4)⋮(2x+1)⇔<3(2x+1)−7>⋮(2x+1)3(2x+1)⋮(2x+1)⇒7⋮(2x+1)⇒2x+1∈−7;−1;1;7⇒2x∈−8;−2;0;6⇒x∈−4;−1;0;3" role="presentation" style="margin: 0px; padding: 1px 0px; display: inline-block; line-height: 0; text-indent: 0px; text-align: left; text-transform: none; font-style: normal; font-weight: normal; font-size: 18.15px; letter-spacing: normal; overflow-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; position: relative;" tabindex="0">⇔(6x−4)⋮(2x+1)
(3x−2)⋮(2x+1)⇔2(3x−2)⋮(2x+1)⇔(6x−4)⋮(2x+1)⇔<3(2x+1)−7>⋮(2x+1)3(2x+1)⋮(2x+1)⇒7⋮(2x+1)⇒2x+1∈−7;−1;1;7⇒2x∈−8;−2;0;6⇒x∈−4;−1;0;3" role="presentation" style="margin: 0px; padding: 1px 0px; display: inline-block; line-height: 0; text-indent: 0px; text-align: left; text-transform: none; font-style: normal; font-weight: normal; font-size: 18.15px; letter-spacing: normal; overflow-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; position: relative;" tabindex="0">⇔<3(2x+1)−7>⋮(2x+1)3(2x+1)⋮(2x+1)
(3x−2)⋮(2x+1)⇔2(3x−2)⋮(2x+1)⇔(6x−4)⋮(2x+1)⇔<3(2x+1)−7>⋮(2x+1)3(2x+1)⋮(2x+1)⇒7⋮(2x+1)⇒2x+1∈−7;−1;1;7⇒2x∈−8;−2;0;6⇒x∈−4;−1;0;3" role="presentation" style="margin: 0px; padding: 1px 0px; display: inline-block; line-height: 0; text-indent: 0px; text-align: left; text-transform: none; font-style: normal; font-weight: normal; font-size: 18.15px; letter-spacing: normal; overflow-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; position: relative;" tabindex="0">⇒7⋮(2x+1)⇒2x+1∈−7;−1;1;7
(3x−2)⋮(2x+1)⇔2(3x−2)⋮(2x+1)⇔(6x−4)⋮(2x+1)⇔<3(2x+1)−7>⋮(2x+1)3(2x+1)⋮(2x+1)⇒7⋮(2x+1)⇒2x+1∈−7;−1;1;7⇒2x∈−8;−2;0;6⇒x∈−4;−1;0;3" role="presentation" style="margin: 0px; padding: 1px 0px; display: inline-block; line-height: 0; text-indent: 0px; text-align: left; text-transform: none; font-style: normal; font-weight: normal; font-size: 18.15px; letter-spacing: normal; overflow-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; position: relative;" tabindex="0">⇒2x∈−8;−2;0;6
(3x−2)⋮(2x+1)⇔2(3x−2)⋮(2x+1)⇔(6x−4)⋮(2x+1)⇔<3(2x+1)−7>⋮(2x+1)3(2x+1)⋮(2x+1)⇒7⋮(2x+1)⇒2x+1∈−7;−1;1;7⇒2x∈−8;−2;0;6⇒x∈−4;−1;0;3" role="presentation" style="margin: 0px; padding: 1px 0px; display: inline-block; line-height: 0; text-indent: 0px; text-align: left; text-transform: none; font-style: normal; font-weight: normal; font-size: 18.15px; letter-spacing: normal; overflow-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; position: relative;" tabindex="0">⇒x∈−4;−1;0;3
Vậyx∈−4;−1;0;3" role="presentation" style="margin: 0px; padding: 1px 0px; display: inline-block; line-height: 0; text-indent: 0px; text-align: left; text-transform: none; font-style: normal; font-weight: normal; font-size: 18.15px; letter-spacing: normal; overflow-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; position: relative;" tabindex="0">x∈−4;−1;0;3