If $a + b + c = 9$ and $a^{2} + b^{2} + c^{2} = 35$ , then find the value of $a^{3} + b^{3} + c^{3} - 3 a b c$

52

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108

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216

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182

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Solution

The correct option is B $108$
$a + b + c = 9$ and $a^{2} + b^{2} + c^{2} = 35$

Using formula,
$(a + b + c)^{2} = a^{2} + b^{2} + c^{2} + 2 (a b + b c + c a)$

$9^{2} = 35 + 2 (a b + b c + c a)$
$2 (a b + b c + c a) = 81 - 35 = 46$
$(a b + b c + c a) = 23$
using formula,
$(a^{3} + b^{3} + c^{3}) - 3 a b c = (a^{2} + b^{2} + c^{2} - a b - b c - c a) (a + b + c)$
$a^{3} + b^{3} + c^{3} - 3 a b c = (35 - 23) \times 9 = 9 \times 12 = 108$
Answer (B) $108$

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Similar questions

If a+b+c =9 and a² + b²+ c²=35 find the value of a³ + b³ + c³ - 3ab

If a + b + c = 9, and $a^{2} + b^{2} + c^{2} = 35$ , find the value of $a^{3} + b^{3} + c^{3} - 3 a b c .$

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

a + b + c = 0

\frac{{(b + c)}^{2}}{3 b c} + \frac{{(c + a)}^{2}}{3 a c} + \frac{{(a + b)}^{2}}{3 a b}

a + b + C = 12

a^{2} + b^{2} + c^{2} = 50

a b + b c + a c

a^{3} + b^{3} + c^{3} - 3 a b c

\frac{a^{3} + b^{3} + c^{3} - 3 a b c}{a b + b c + c a - a^{2} - b^{2} - c^{2}}

a = - 5, b = - 6, c = 10

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