△ABC的面积为S,外接圆半径R=√17,a,b,c分别是角A、B、C的对边,设S=a^2-(b-c)^2,sinB+s

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  • sinB+sinC= b/2R+c/2R=8/(√17) b+c=16

    S=a^2-(b-c)^2=√[p(p-a)(p-b)(p-c)] p=(a+b+c)/2

    即 (a+b-c)(a-b+c) = 1/4×√((a+b+c)(a+b-c)(a-b+c)(b+c-a)

    16(a+b-c)(a-b+c)=(a+b+c)(b+c-a)

    a^2 = b^2+c^2-30/17×bc = b^2+c^2-2bccosA

    cosA = 15/17

    sinA = 8/17

    a = 2RsinA = 16/(√17)

    设 bc = x

    a^2-(b-c)^2 = a^2 + 4bc - (b+c)^2 = bcsinA/2

    4x + 16^2/17 - 16^2 = 4/17x

    x = 64

    S = bcsinA/2 = 256/17