If in a A B C, r₁=2, r₂=3 and r₃=6 , then a equals to

Step-by-step solution

Given, r₁=2, r₂=3 and r₃=6 aligned & r₁= s-a 2= s-a & s-a = 1 2 & r₂= s-b 3= s-b & s-b = 1 3 & and & r₃= s-c 6= s-C & s-c 4 = 1 6 & aligned On adding Eqs. (i), (ii) and (iii), we get aligned & s-a + (s-b) 4 + s-c = 1 2 + 1 3 + 1 6 & 3 s-(a+b+c) 4 = 3+2+1 6 & 3 s-2 s 4 = 6 6 =0 & s =1 & s^2=r₁ r₂+r₂ r₃+r₃ r₁ aligned aligned & =2 3+3 6+6 2 & =6+18+12=36 s^2 & =36 s=6 aligned From Eq. (i), we get aligned 6 & =1 Now, r₁ & = s-a 2 & = 6 6-a 6-a & =3 a=3 aligned