What is the value of 8 a 3-27 b 3- c 3 if 2 a -3 b - c -0 -A- 12 abcB- 18 abcC- 6 abcD- 48 abc

The correct option is B 18abcWe know, if x + y + z = 0; x^3 + y^3 + z^3 = 3xyz Here, nbsp;x = 2a , y = 3b , z = c Given 2a + 3b + c = 0 ⇒ (2a)^3 + (3b)^3 ...

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Byju's Answer

Standard IX

Mathematics

Identity (x)^3+(y)^3+(z)^3-3xyz

What is the v...

Question

What is the value of $8 a^{3} + 27 b^{3} + c^{3}$ if $2 a + 3 b + c = 0$ ?

48 a b c

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6 a b c

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18 a b c

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12 a b c

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Solution

The correct option is C $18 a b c$
We know,
if $x + y + z = 0$ ; $x^{3} + y^{3} + z^{3} = 3 x y z$

Here,
x = 2a , y = 3b , z = c

Given
$2 a + 3 b + c = 0$

$\Rightarrow$ $(2 a)^{3} + (3 b)^{3} + c^{3} = 3 (2 a) (3 b) (c)$

$\Rightarrow$ $18 a b c$

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Similar questions

Q. If

2 a + 3 b + c = 0

then show that:

8 a^{3} + 27 b^{3} + c^{3} = 18 a b c

If $2 a - 3 b = - 1$ and $a b = 12$

then

$8 a^{3} - 27 b^{3} =$

If $(8 a^{3} + 27 b^{3}) = 0$

then

$(4 a^{2} + 9 b^{2}) =$

Q. State whether the statement is True or False.

The cube of

(2 a + 3 b)

is equal to

8 a^{3} + 36 a^{2} b + 54 a b^{2} + 27 b^{3}

Q. State whether the statement is True or False.

The cube of

(3 b - 2 a)

is equal to

27 b^{3} - 54 b^{2} a + 36 b a^{2} - 8 a^{3}

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What is the value of 8a3+27b3+c3 if 2a+3b+c=0?

The correct option is C 18abcWe know, if x+y+z=0; x3+y3+z3=3xyz Here, x = 2a , y = 3b , z = c Given 2a+3b+c=0 ⇒ (2a)3+(3b)3+c3=3(2a)(3b)(c) ⇒18abc

What is the value of $8 a^{3} + 27 b^{3} + c^{3}$ if $2 a + 3 b + c = 0$ ?

The correct option is C $18 a b c$
We know,
if $x + y + z = 0$ ; $x^{3} + y^{3} + z^{3} = 3 x y z$

Here,
x = 2a , y = 3b , z = c

Given
$2 a + 3 b + c = 0$

$\Rightarrow$ $(2 a)^{3} + (3 b)^{3} + c^{3} = 3 (2 a) (3 b) (c)$

$\Rightarrow$ $18 a b c$