Question

If 3a+5b+4c=0 then show that : 27a^3+125a^3+64c^3=180 abc

Answer 1

Heya ✋

Let see your answer !!!!!

Given that

3a + 5b + 4c = 0

We have to prove that

27a^3 + 125a^3 + 64c^3 = 180abc

Solution

3a + 5b + 4c = 0

=> 3a + 5b = -4c

Cubing both sides

=> (3a + 5b)^3 = (-4c)^3 ----------- (i)

=> (3a)^3 + (5b)^3 + 3 × 3a × 5b(3a + 5b) = -64c^3

=> 27a^3 + 125b^3 + 45ab(3a + 5b) = -64c^3

=> 27a^3 + 125b^3 + 45ab(-4c) = -64c^3

=> 27a^3 + 125b^3 - 180abc = -64c^3

=> 27a^3 + 125b^3 + 64c^3 = 180abc

Proved

Thanks :)))))

Answer 2

Step-by-step explanation:

hope this will help you