The value of 1- r 12-1- r 22-1- r 32-1- r 2 iA- 0B- a2-b2-c2-2C- -2-a2-b2-c2D- a2-b2-c2-

The correct option is B Since, nbsp;1/r_1^2=(s a)^2/Δ ^2, nbsp;1/r_2^2=(s b)^2/Δ ^2, nbsp;1/r_3^2=(s c)^2/Δ ^2, and 1/r^2=s^2/Δ ^2 ∴1/r_1^2+1/r_2^2+1/r_3 ...

333

You visited us 333 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard XI

Mathematics

Sum of product of binomial coefficients

The value of ...

Question

The value of $\frac{1}{r_{1}^{2}} + \frac{1}{r_{2}^{2}} + \frac{1}{r_{3}^{2}} + \frac{1}{r^{2}}$ is

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is B

Since, $\frac{1}{r_{1}^{2}} = \frac{(s - a)^{2}}{Δ^{2}}, \frac{1}{r_{2}^{2}} = \frac{(s - b)^{2}}{Δ^{2}}, \frac{1}{r_{3}^{2}} = \frac{(s - c)^{2}}{Δ^{2}}, a n d \frac{1}{r^{2}} = \frac{s^{2}}{Δ^{2}} ∴ \frac{1}{r_{1}^{2}} + \frac{1}{r_{2}^{2}} + \frac{1}{r_{3}^{2}} + \frac{1}{r^{2}} = \frac{s^{2} + (s - a)^{2} + (s - b)^{2} + (s - c)^{2}}{Δ^{2}} = \frac{4 s^{2} + a^{2} + b^{2} + c^{2} - 2 s (a + b + c)}{Δ^{2}} = \frac{a^{2} + b^{2} + c^{2}}{Δ^{2}}$

Suggest Corrections

Similar questions

In any $△ A B C, \frac{1}{r_{1}^{2}} + \frac{1}{r_{2}^{2}} + \frac{1}{r_{3}^{2}} + \frac{1}{r^{2}}$ is equal to

\frac{Δ^{2}}{a^{2} + b^{2} + c^{2}} {\frac{1}{r_{1}^{2}} + \frac{1}{r_{2}^{2}} + \frac{1}{r_{3}^{2}} + \frac{1}{r^{2}}} =

Q. Simplify

r^{2} + r_{1}^{2} + r_{2}^{2} + r_{3}^{2} = 16 R^{2} - a^{2} - b^{2} - c^{2}

Q. If

\frac{a^{2}}{r_{1}^{2}} + \frac{b^{2}}{r_{2}^{2}} + \frac{c^{2}}{r_{3}^{2}} = k

, then

Q. If

a + b + c = 0

then

\frac{1}{b^{2} + c^{2} - a^{2}} + \frac{1}{c^{2} + a^{2} - b^{2}} + \frac{1}{a^{2} + b^{2} - c^{2}}

is equal to

Join BYJU'S Learning Program

The value of 1r21+1r22+1r23+1r2 is

The correct option is B Since, 1r21=(s−a)2Δ2,1r22=(s−b)2Δ2,1r23=(s−c)2Δ2,and 1r2=s2Δ2∴1r21+1r22+1r23+1r2=s2+(s−a)2+(s−b)2+(s−c)2Δ2=4s2+a2+b2+c2−2s(a+b+c)Δ2=a2+b2+c2Δ2

The value of $\frac{1}{r_{1}^{2}} + \frac{1}{r_{2}^{2}} + \frac{1}{r_{3}^{2}} + \frac{1}{r^{2}}$ is