Question

plz ans it......
I will surely mark as Brainliest. ​

Answer 1

Solution of the given problem :

The coordinates of the vertices P, Q, R of ΔPQR are P (a, b), Q (b, c), R (c, a).

1st proof.

Here, the coordinates of the centroid are

( (a + b + c)/3, (b + c + a)/3 )

By the given condition,

( (a + b + c)/3, (b + c + a)/3 ) = (0, 0)

∴ a + b + c = 0.

2nd proof.

Now, a³ + b³ + c³

= (a + b + c) (a² + b² + c² - ab - bc - ca) + 3abc

= 0 × (a² + b² + c² - ab - bc - ca) + 3abc,

since a + b + c = 0

= 0 + 3abc

= 3abc

i.e., a³ + b³ + c³ = 3abc ..... (1)

Now, a²/(bc) + b²/(ca) + c²/(ab)

= (a³ + b³ + c³)/(abc)

= (3abc) / (abc), by (1)

= 3

∴ a²/(bc) + b²/(ca) + c²/(ab) = 3