In a A B C , if a^2+b^2+c^2=a c+ 3 a b , then the triangle is

Step-by-step solution

We have, a^2+b^2+c^2=a c+ 3 a b aligned & a^2 4 +c^2-a c+ 3 a^2 4 +b^2- 3 a b=0 & ( a 2 -c )^2+ ( 3 a 2 -b )^2=0 aligned array ll & a 2 -c=0 and 3 2 a-b=0 & a=2 c and 3 a=2 b & a= 2 b 3 =2 c= & a= , b= 3 2 and c= 2 array Now, b^2+c^2= ( 3 2 )^2+ ( 2 )^2= 3 ^2 a + ^2 4 = ^2 b^2+c^2=a^2 Hence, the triangle is right angled but not isosceles.