Question

打问号的三题，高一数学的

Answer 1

7
cos^2A+cos^2B+cos^2C=1

cos^2B+cos^2C=1-cos^2A

cos^2B+cos^2C=sin^2A

cos^2B+cos^2C=sin^2(B+C)

cos^2B+cos^2C=sin^2Bcos^2C+2(sinBcosCcosBsinC)+cos^2Bsin^2C

cos^2B+cos^2C-(sin^2Bcos^2C+cos^2Bsin^2C)=2(sinBcosCcosBsinC)

cos^2Bcos^2C+cos^2Ccos^2B=2(sinBcosCcosBsinC)

即cosBcosC=sinBsinC
即tanBtanC=1
所以B+C=90°
△ABC的形状是直角三角形

8
如果C为直角。那么c=√13 所以c最大值为√13
假设B为直角。那么c=√5 所以c最小 值为√5

9
a^4+b^4+c^4=2c^2(a^2+b^2)
a^4+b^4+c^4+2a^2b^2-2b^2c^2-2a^2c^2=2a^2b^2
(a^2+b^2-c^2)^2=2a^2b^2
(a^2+b^2-c^2)/(ab)=√2或-√2
cos∠c=(a^2+b^2-c^2)/(2ab)=√2/2或-√2/2
即cos∠c=π/4或3π/4