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slamgirl [31]
3 years ago
12

Giải phương trình: Sin^4 x - cos^4 x =1/2

Mathematics
2 answers:
tamaranim1 [39]3 years ago
5 0

Hello,

cos^4(x)=(cos^2(x))^2=(1-sin^2(x))^2=1+sin^4(x)-2*sin^2(x)\\\\sin^4(x)-(1+sin^4(x)-2sin^2(x))=\dfrac{1}{2} \\\\1-2sin^2(x)=\dfrac{1}{2} \\\\\\sin^2(x)=\dfrac{1}{4} \\\\sin(x)=\dfrac{1}{2} \ or\ sin(x)=-\dfrac{1}{2} \\\\\\modulo\ 2\pi: \\\\x=\dfrac{\pi}{6}\ or\ x=\dfrac{5*\pi}{6}\ or\ x=-\dfrac{\pi}{6}\ or\ x=-\dfrac{5*\pi}{6}

Sliva [168]3 years ago
4 0

Step-by-step explanation:

...........MaRk As BrAiNeSt

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Answer:

The maximum volume of such box is 32m^3

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Step-by-step explanation:

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To be able to maximize the volume, we need to reduce the number of variables.

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