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AP EAMCET202124 Aug 2021Evening ShiftMathematicsProperties of TrianglesActual

What is the greatest angle of the triangle whose sides are x^2+x+1,2 x+1, x^2-1 ?

Options

  1. AA=120^
  2. BA=90^
  3. CA=135^
  4. DA=60^

Correct answer

A. A=120^

Step-by-step solution

Sides of triangle are aligned & x^2+x+1,2 x+1 and x^2-1 & x^2+x+1 is the greatest side. aligned A= b^2+c^2-a^2 2 b c Here, a=x^2+x+1, b=2 x+1, c=x^2-1 A= (2 x+1)^2+ (x^2-1 )^2- (x^2+x+1 )^2 2(2 x+1) (x^2-1 ) A= .(2 x+1)^2+(x^2-1+x^2+x+1(x^2-1-x^2-x-1 ) 2(2 x+1) (x^2-1 ) aligned & A= (2 x+1)^2+ (2 x^2+x )(-x-2) 2(2 x+1) (x^2-1 ) & A= (2 x+1) (2 x+1-x^2-2 x ) 2(2 x+1) (x^2-1 ) aligned A= -(2 x+1) (x^2-1 ) 2(2 x+1) (x^2-1 ) = -1 2 A=120^

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