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Question

In ABC, if tanA2 and tanA2 are the roots of the equation 6x25x+1=0, then

A
a2+b2>c2
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B
a2b2=c2
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C
a2+b2=c2
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D
None of these
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Solution

The correct option is C a2+b2=c2
If tan A/2 and tan B/2 are the roots of the eqn 6x25x+1=0, Then

tanA/2+tanB/2=5/6tanA/2.tanB/2=1/6

tan(A/2+B/2)=tanA/2+tanB/21tanA/2.tanB/2=5/611/6=1

A2+B2=π4

A+B=π2

C=π2

ABC is right angle triangle

c2=a2+b2

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