Question : If $(a + b + c) = 20$ and $a^{2} + b^{2} + c^{2} = 152$ , find the value of $a^{3} + b^{3} + c^{3} - 3 a b c$ .
Option 1: 560
Option 2: 640
Option 3: 480
Option 4: 720

Question

Question : If $a + b - c = 20$ and $a^{2} + b^{2} + c^{2} = 152$ , find the value of $a^{3} + b^{3} - c^{3} + 3 a b c$ .

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Answer 1

Correct Answer: 560

Solution : Given: $(a + b + c) = 20$ and $a^{2} + b^{2} + c^{2} = 152$
We know the identity,
$(a + b + c)^{2} = a^{2} + b^{2} + c^{2} + 2 a b + 2 b c + 2 c a$
$(a + b + c)^{2} = a^{2} + b^{2} + c^{2} + 2 (a b + b c + c a)$
⇒ $20^{2} = 152 + 2 (a b + b c + c a)$
⇒ $a b + b c + c a = \frac{400 - 152}{2}$
⇒ $a b + b c + c a = 124$ .........(i)
Also,
$a^{3} + b^{3} + c^{3} - 3 a b c = (a + b + c) (a^{2} + b^{2} + c^{2} - a b - b c - c a)$
From (i),
$a^{3} + b^{3} + c^{3} - 3 a b c = (20) (152 - 124)$
⇒ $a^{3} + b^{3} + c^{3} - 3 a b c = 560$
Hence, the correct answer is 560.

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Question : If (a+b+c)=20 and a2+b2+c2=152, find the value of a3+b3+c3−3abc.Option 1: 560Option 2: 640Option 3: 480Option 4: 720

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Question : If $(a + b + c) = 20$ and $a^{2} + b^{2} + c^{2} = 152$ , find the value of $a^{3} + b^{3} + c^{3} - 3 a b c$ .
Option 1: 560
Option 2: 640
Option 3: 480
Option 4: 720