Question

if 3a + 5b + 4c =0 show that 273 +125b3 +64c3 =180abc

Answer 1

Answer:

$we \: know \: if \: x + y + z = 0 \: then \: {x}^{3} + {y}^{3} + {z}^{3} = 3xyz \\ put \: x = 3a \\ y = 5b \\ z = 4c \\ then \: {(3a)}^{3} + {(5b)}^{3} + {(4c)}^{3} = 3 \times 3a \times 5b \times 4c \\ 27{a}^{3} + 125 {b}^{3} + 64{c}^{3} = 180abc$