Let A B C be a triangle such that A C B= 6 and let a, b and c denote the lengths of the sides opposite to A, B and C respectively. The value(s) of x for which a=x^2+x+1, b=x^2-1 and c=2 x+1 is (are)

Step-by-step solution

Using, C= a^2+b^2-c^2 2 a b gathered 3 2 = (x^2+x+1 )^2+ (x^2-1 )^2-(2 x+1)^2 2 (x^2+x+1 ) (x^2-1 ) (x+2)(x+1)(x-1) x+ (x^2-1 )^2 = 3 (x^2+x+1 ) (x^2-1 ) x^2+2 x+ (x^2-1 )= 3 (x^2+x+1 ) (2- 3 ) x^2+(2- 3 ) x-( 3 +1)=0 gathered x=-(2+ 3 ) and x=1+ 3 But, x=-(2+ 3 ) c is negative. x=1+ 3 is the only solution. Hence, (b) is the correct option.