giải các phương trình sau:
1. cos3x-cos4x+cos5x=0
2.cos2x-cosx=2sin^2 3x/2
3. sin^4x +cos^4x=-1/2cos^2.2x câu hỏi 2729094 - hoidap247.com

Question

giải các phương trình sau:
1. cos3x-cos4x+cos5x=0
2.cos2x-cosx=2sin^2 3x/2
3. sin^4x +cos^4x=-1/2cos^2.2x

hetsot2k7 · Answer

Đáp án:   Giải thích các bước giải:

khanhan164218 · Answer

Đáp án:
{4x=&#x03C0;2+k&#x03C0;x=&#xB1;&#x03C0;3+k2&#x03C0;" role="presentation" style="margin: 0px; padding: 0px; display: inline; font-style: normal; font-weight: normal; line-height: normal; font-size: 15px; text-indent: 0px; text-align: left; text-transform: none; letter-spacing: normal; word-spacing: normal; overflow-wrap: 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">⎧⎩⎨⎪⎪4x=π2+kπx=±π3+k2π{4x=π2+kπx=±π3+k2π (k&#x2208;Z)" role="presentation" style="margin: 0px; padding: 0px; display: inline; font-style: normal; font-weight: normal; line-height: normal; font-size: 15px; text-indent: 0px; text-align: left; text-transform: none; letter-spacing: normal; word-spacing: normal; overflow-wrap: 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">(k∈Z)(k∈Z)
Lời giải:
cos&#x2061;3x&#x2212;cos&#x2061;4x+cos&#x2061;5x=0" role="presentation" style="margin: 0px; padding: 0px; display: inline; font-style: normal; font-weight: normal; line-height: normal; font-size: 15px; text-indent: 0px; text-align: left; text-transform: none; letter-spacing: normal; word-spacing: normal; overflow-wrap: 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">cos3x−cos4x+cos5x=0cos⁡3x−cos⁡4x+cos⁡5x=0
Sử dụng công thức biến đổi thổng thành tích ta có phương trình tương đương:
(cos&#x2061;3x+cos&#x2061;5x)&#x2212;cos&#x2061;4x=0" role="presentation" style="margin: 0px; padding: 0px; display: inline; font-style: normal; font-weight: normal; line-height: normal; font-size: 15px; text-indent: 0px; text-align: left; text-transform: none; letter-spacing: normal; word-spacing: normal; overflow-wrap: 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">(cos3x+cos5x)−cos4x=0(cos⁡3x+cos⁡5x)−cos⁡4x=0
&#x21D4;2cos&#x2061;4xcos&#x2061;x&#x2212;cos&#x2061;4x=0" role="presentation" style="margin: 0px; padding: 0px; display: inline; font-style: normal; font-weight: normal; line-height: normal; font-size: 15px; text-indent: 0px; text-align: left; text-transform: none; letter-spacing: normal; word-spacing: normal; overflow-wrap: 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">⇔2cos4xcosx−cos4x=0⇔2cos⁡4xcos⁡x−cos⁡4x=0
&#x21D4;" role="presentation" style="margin: 0px; padding: 0px; display: inline; font-style: normal; font-weight: normal; line-height: normal; font-size: 15px; text-indent: 0px; text-align: left; text-transform: none; letter-spacing: normal; word-spacing: normal; overflow-wrap: 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">⇔⇔[cos&#x2061;4x=0cos&#x2061;x=12" role="presentation" style="margin: 0px; padding: 0px; display: inline; font-style: normal; font-weight: normal; line-height: normal; font-size: 15px; text-indent: 0px; text-align: left; text-transform: none; letter-spacing: normal; word-spacing: normal; overflow-wrap: 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">⎡⎣cos4x=0cosx=12[cos⁡4x=0cos⁡x=12 
&#x21D4;" role="presentation" style="margin: 0px; padding: 0px; display: inline; font-style: normal; font-weight: normal; line-height: normal; font-size: 15px; text-indent: 0px; text-align: left; text-transform: none; letter-spacing: normal; word-spacing: normal; overflow-wrap: 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">⇔⇔[4x=&#x03C0;2+k&#x03C0;x=&#xB1;&#x03C0;3+k2&#x03C0;" role="presentation" style="margin: 0px; padding: 0px; display: inline; font-style: normal; font-weight: normal; line-height: normal; font-size: 15px; text-indent: 0px; text-align: left; text-transform: none; letter-spacing: normal; word-spacing: normal; overflow-wrap: 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">⎡⎣⎢4x=π2+kπx=±π3+k2π[4x=π2+kπx=±π3+k2π (k&#x2208;Z)" role="presentation" style="margin: 0px; padding: 0px; display: inline; font-style: normal; font-weight: normal; line-height: normal; font-size: 15px; text-indent: 0px; text-align: left; text-transform: none; letter-spacing: normal; word-spacing: normal; overflow-wrap: 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">(k∈Z)(k∈Z)
Vậy phương trình trên có 2 nghiệm là:
{4x=&#x03C0;2+k&#x03C0;x=&#xB1;&#x03C0;3+k2&#x03C0;" role="presentation" style="margin: 0px; padding: 0px; display: inline; font-style: normal; font-weight: normal; line-height: normal; font-size: 15px; text-indent: 0px; text-align: left; text-transform: none; letter-spacing: normal; word-spacing: normal; overflow-wrap: 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">⎧⎩⎨⎪⎪4x=π2+kπx=±π3+k2π{4x=π2+kπx=±π3+k2π (k&#x2208;Z)" role="presentation" style="margin: 0px; padding: 0px; display: inline; font-style: normal; font-weight: normal; line-height: normal; font-size: 15px; text-indent: 0px; text-align: left; text-transform: none; letter-spacing: normal; word-spacing: normal; overflow-wrap: 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">(k∈Z)(k∈Z).

giải các phương trình sau: 1. cos3x-cos4x+cos5x=0 2.cos2x-cosx=2sin^2 3x/2 3. sin^4x +cos^4x=-1/2cos^2.2x

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giải các phương trình sau: 1. cos3x-cos4x+cos5x=0 2.cos2x-cosx=2sin^2 3x/2 3. sin^4x +cos^4x=-1/2cos^2.2x

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