Question

plz solve it friends.. plz simplify it

Answer 1

use the formulas attached and reduce

Answer 2

HOLA !!

ANSWER...

(a² - b²)³ + (b² - c²)³ + (c² - a²)³ / (a - b)³ + (b - c)³ + (c - a)³

Let,

a² - b² = x

b² - c² = y

c² - a² = z

So,

x + y + z = 0

x³ + y³ + z³ = 3xyz ---------(i)

Putting the value of x , y and z in the above equation.

(a² - b²)³ + (b² - c²)³ + (c² - a²)³ = 0

(a² - b²) + (b² - c²) + (c² - a²)

∴3(a² - b²) (b² - c²) (c² - a²).............(ii)

Again,Let,

a - b = p

b - c = q

c - a = r

Since,

p + q + r = 0

p³ + q³ + r³ = 3pqr --------(iii)

Putting the value of p , q and r in the above equation.

(a - b) + (b - c) + (c - a) = 0

(a - b)³ + (b - c)³ + (c - a)³ =

∴3(a - b) (b - c) (c - a).............(iv)

From equation (ii) and (iv),

We get,

(a² - b²)³ + (b² - c²)³ + (c² - a²)³ / (a - b)³ + (b - c)³ + (c - a)³ =

3(a² - b²) (b² - c²) (c² - a²)/3(a - b) (b - c) (c - a)

= 3(a + b) (b + c) (c + a)..