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Question

Let cos1(x)+cos1(2x)+cos1(3x) be π If x satisfies the equation ax3+bx2+cx1=0, then the value of (bac) is

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Solution

cos1(x)+cos1(2x)+cos1(3x)=π
cos1(x)+cos1(2x)=πcos1(3x)
cos1(x(2x)1x214x2)=πcos1(3x)
Taking cosθ on both sides , we get
2x21x214x2=3x
2x2+3x=1x214x2
4x4+9x2+12x3=(1x2)(14x2)
4x4+12x3+9x2=15x2+4x4
12x3+14x21=0
ax3+bx2+cx1=0
Hence
a=12,b=14,c=0
Hence b(a+c)
=1412
=2

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