State true or false:

If $a + 2 b = 5$ ; then

$a^{3} + 8 b^{3} + 30 a b = 125$

True

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False

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Solution

The correct option is A True
$a + 2 b = 5$
$=> a + 2 b - 5 = 0$
If $a + b + c = 0, t h e n a^{3} + b^{3} + c^{3} = 3 a b c$
Cubing both sides,
$=> a^{3} + (2 b)^{3} - 5^{3} = 3 (a) (2 b) (- 5)$
$=> a^{3} + 8 b^{3} - 125 = - 30 a b$
$=> a^{3} + 8 b^{3} + 30 a b = 125$

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Similar questions

a + 2 b + c = 0

a^{3} + 8 b^{3} + c^{3} = 6 a b c

a^{3} + 8 b^{3} + 30 a b

{(a + \frac{1}{a})}^{2} = 3

a \neq 0

a^{3} + \frac{1}{a^{3}} = 0

a_{1}, a_{2}, a_{3} \in + R

\frac{a_{1}}{a_{2}} + \frac{a_{2}}{a_{3}} + \frac{a_{3}}{a_{1}} \geq 3

a + \frac{1}{a} = p

a \neq 0

a^{3} + \frac{1}{a^{3}} = p (p^{2} - 3)

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