If 3 a-5 b-4 c-0- Find the value of 27 a3-125 b3-64 c3A- 0B- 1C- -180 abcD- -180 abc

The correct option is D +180 abc 3a + 5b + 4c = 0. ⇒ 3a + 5b = 4c —— (1) Cabing both sides, we get. (3a + 5b)^3 = ( 4c)^3 ⇒ (3a)^3 + (5b)^3 + 3 × 3 ...

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Byju's Answer

Standard IX

Mathematics

Algebraic Identities

If 3 a+5 b+4 ...

Question

If 3a + 5b + 4c = 0, Find the value of $27 a^{3} + 125 b^{3} + 64 c^{3}$ .

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-180 abc

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+180 abc

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Solution

The correct option is D
+180 abc

$3 a + 5 b + 4 c = 0$ .

$\Rightarrow 3 a + 5 b = - 4 c$ -------(1)

Cabing both sides, we get.

$(3 a + 5 b)^{3} = (- 4 c)^{3}$

$\Rightarrow (3 a)^{3} + (5 b)^{3} + 3 \times 3 a \times 5 b \times (3 a + 5 b) = - 64 c^{3}$

$\Rightarrow 27 a^{3} + 125 b^{3} + 45 a b (3 a + 5 b) = - 64 c^{3}$

$\Rightarrow 27 a^{3} + 125 b^{3} + 45 a b (- 4 c) = - 64 c^{3}$ -----from eq (1)

$\Rightarrow 27 a^{3} + 125 b^{3} + 64 c^{3} = - 45 a b (- 4 c)$

$27 a^{3} + 125 b^{3} + 64 c^{3} = + 180 a b c$ .

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Q. If 3a + 5b + 4c = 0; then the value of 27a³ + 125b³ + 64c³
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If $3 a + 5 b + 4 c = 0$ , show that:
$27 a^{3} + 125 b^{3} + 64 c^{3} = 180 a b c$ .

State true or false:

3 a + 5 b + 4 c = 0

, then

27 a^{3} + 125 b^{3} + 64 c^{3} = 180 a b c

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If 3a + 5b + 4c = 0, Find the value of 27a3+125b3+64c3.

If 3a + 5b + 4c = 0, Find the value of $27 a^{3} + 125 b^{3} + 64 c^{3}$ .