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Question:

LetABCbe a triangle such that∠ACB=Ο€6and leta, bandcdenote the lengths of the sides opposite toA, BandCrespectively. The value(s) of x for whicha=x2+x+1, b=x2π•’΅andc=2x+1is (are)βˆ’(2+√3)1+√32+√34√3LetABCbe a triangle such that∠ACB=Ο€6and leta, bandcdenote the lengths of the sides opposite toA, BandCrespectively. The value(s) of x for whicha=x2+x+1, b=x2π•’΅andc=2x+1is (are)βˆ’(2+√3)1+√32+√34√3ABCABCABCAABBCC∠ACB=Ο€6∠ACB=Ο€6∠ACB=Ο€6∠∠AACCBB==Ο€6Ο€6Ο€6Ο€6πππ666a, ba, ba, baa,, bbcccccA, BA, BA, BAA,, BBCCCCCa=x2+x+1, b=x2π•’΅a=x2+x+1, b=x2π•’΅a=x2+x+1, b=x2π•’΅aa==x2xxx22222++xx++11,, bb==x2xxx22222βˆ’π•’΅1c=2x+1c=2x+1c=2x+1cc==22xx++11βˆ’(2+√3)βˆ’(2+√3)βˆ’(2+√3)βˆ’(2+√3)βˆ’βˆ’((22++√3√3√√3333))1+√31+√31+√31+√311++√3√3√√33332+√32+√32+√32+√322++√3√3√√33334√34√34√34√344√3√3√√3333A1+√31+√31+√31+√31+√311++√3√3√√3333Bβˆ’(2+√3)βˆ’(2+√3)βˆ’(2+√3)βˆ’(2+√3)βˆ’(2+√3)βˆ’βˆ’((22++√3√3√√3333))C4√34√34√34√34√344√3√3√√3333D2+√32+√32+√32+√32+√322++√3√3√√3333?

1+√3

βˆ’(2+√3)

4√3

2+√3

Solution:

The correct option is B1+√3Using cosine rule for∠Ccos∠C=a2+b2βˆ’c22ab