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Question

If α,β are the roots of the equation (tan1(x/5))2+(31)tan1(x/5)3=0,|α|>|β| then

A
α+β=5π/12
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B
|αβ|=35π/12
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C
αβ=25π2/12
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D
3α+4β=0
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Solution

The correct options are
A 3α+4β=0
B |αβ|=35π/12
C αβ=25π2/12
D α+β=5π/12
(tan1(x/5)+3)(tan1(x/5)1)=0
tan1(x/5)=3x5=π3x=5π3
and tan1(x/5)=1x5=π4x=5π4
Let α=5π3,β=5π4
α+β=5π/12,|αβ|=35π/12
αβ=25π2/12 and 3α+4β=0

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