If $a + b + c = 10, a^{2} + b^{2} + c^{2} = 38$ and $a^{3} + b^{3} + c^{3} = 160$ , find the value of $a b c$

45

No worries! We‘ve got your back. Try BYJU‘S free classes today!

15

No worries! We‘ve got your back. Try BYJU‘S free classes today!

10

No worries! We‘ve got your back. Try BYJU‘S free classes today!

30

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

Open in App

Solution

The correct option is D $30$
$(a + b + c) = 10; a^{2} + b^{2} + c^{2} = 38$ & $a^{3} + b^{3} + c^{3} = 160$

$(a + b + c)^{2} = a^{2} + b^{2} + c^{2} + 2 (a b + b c + a c) \Rightarrow \frac{100 - 38}{2} = a b + b c + c a$

$\Rightarrow a b + b c + c a = 31$

As $a^{3} + b^{3} + c^{3} - 3 a b c = (a + b + c) [a^{2} + b^{2} + c^{2} - a b - b c - c a]$

$160 - 3 a b c = 10 [38 - 31]$

$\Rightarrow \frac{160 - 70}{3} = a b c \Rightarrow a b c = 30$

Suggest Corrections

Similar questions

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

\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

\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

If $a + b + c = 15$ and $a^{2} + b^{2} + c^{2} = 83$ then find the value of $a^{3} + b^{3} + c^{3} - 3 a b c$

a + b + c = 6, a^{2} + b^{2} + c^{2} = 14 and a^{3} + b^{3} + c^{3} = 36

a b c

Join BYJU'S Learning Program