Prove that r1r2-r2r3-r3r1-1-4 a-b-c 2

L.H.S =r_1r_2+r_2r_3+r_3r_1 We know r_1=Δs a, r_2 =Δs b, r_3 = Δs c, r = Δs =Δ^2/(s a)(s b)+Δ^2/(s b)(s c)+Δ^2/(s c)(s a) = s(s c)+s(s a)+s( ...

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Heat of Reaction

Prove that ...

Question

Prove that $r_{1} r_{2} + r_{2} r_{3} + r_{3} r_{1} = \frac{1}{4} {(a + b + c)}^{2}$

Open in App

Solution

Suggest Corrections

Similar questions

r_{1} (r_{2} + r_{3}) / a = r_{2} (r_{3} + r_{1}) / b = r_{3} (r_{1} + r_{2}) / c

a (r r_{1} + r_{2} r_{3}) = b (r r_{2} + r_{3} r_{1}) = c (r r_{3} + r_{1} r_{2}) = a b c

\frac{r_{1} (r_{2} + r_{3})}{\sqrt{r_{1} r_{2} + r_{2} r_{3} + r_{3} r_{1}}} =

\frac{r_{1} (r_{2} + r_{3})}{\sqrt{r_{1} r_{2} + r_{2} r_{3} + r_{3} r_{1}}} = a

In a $△ A B C, r_{1} r_{2} + r_{2} r_{3} + r_{3} r_{1} =$

Join BYJU'S Learning Program