Question

❤${\bold{\purple{\small{Hey Frndz}}}}$❤

If
$3a + 2b = 5c \: and \: abc = 4$

Find the value of :
$27 {a}^{3} + 8 {b}^{3} - 125 {c}^{3}$
​

Answer 1

Answer:

-360

Step-by-step explanation:

Given Equation is 3a + 2b = 5c.

On cubing both sides, we get

⇒ (3a + 2b)³ = (5c)³

⇒ 27a³ + 8b³ + 3(3a)(2b)(3a + 2b) = 125c³

⇒ 27a³ + 8b³ + 18ab(5c) = 125c³

⇒ 27a³ + 8b³ + 90abc = 125c³

Given, abc = 4

⇒ 27a³ + 8b³ + 90(4) = 125c³

⇒ 27a³ + 8b³ - 125c³ = -360.

Hope it helps!

Answer 2

$\huge\bf\mathscr\pink{Your\: Answer}$

-360

step-by-step explanation:

Given,

$3a + 2b = 5c \: and \: abc = 4$

On cubing both sides,

we get,

⇒ (3a + 2b)³ = (5c)³

expanding the equation,

we get,

⇒ 27a³ + 8b³ + 3(3a)(2b)(3a + 2b) = 125c³

But, it is given,

( 3a + 2b ) = 5c

Putting this value in the equation,

we get,

⇒ 27a³ + 8b³ + 18ab(5c) = 125c³

⇒ 27a³ + 8b³ + 90abc = 125c³

Again,

It is given that,

abc = 4

Putting this value in the equation,

we get,

⇒ 27a³ + 8b³ + 90(4) = 125c³

⇒ 27a³ + 8b³ - 125c³ = -360.