Question : What will be the value of $x^{3} + y^{3} + z^{3} - 3 x y z$ , when $x + y + z = 9$ and $x^{2} + y^{2} + z^{2} = 31 ?$
Option 1: 27
Option 2: 3
Option 3: 54
Option 4: 9

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Question : If $x + y + z = 13, x^{2} + y^{2} + z^{2} = 133$ and $x^{3} + y^{3} + z^{3} = 847$ , then the value of $\sqrt[3]{x y z}$ is:

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Answer 1

Correct Answer: 54

Solution : Give: $x + y + z = 9$ ......(1)
$x^{2} + y^{2} + z^{2} = 31$ ......(2)
As $(a + b + c)^{2} = a^{2} + b^{2} + c^{2} + 2 (a b + b c + c a)$
Squaring (1) on both sides, we have,
$(x + y + z)^{2} = 81$
⇒ $x^{2} + y^{2} + z^{2} + 2 (x y + y z + z x) = 81$
⇒ $31 + 2 (x y + y z + z x) = 81$
⇒ $x y + y z + z x = 25$
Now, $x^{3} + y^{3} + z^{3} - 3 x y z$
= $(x + y + z) (x^{2} + y^{2} + z^{2} - x y - y z - z x)$
= $(9) (31 - 25) = 9 \times 6 = 54$
Hence, the correct answer is 54.

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Question : What will be the value of x3+y3+z3−3xyz, when x+y+z=9 and x2+y2+z2=31?Option 1: 27Option 2: 3Option 3: 54Option 4: 9

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Question : What will be the value of $x^{3} + y^{3} + z^{3} - 3 x y z$ , when $x + y + z = 9$ and $x^{2} + y^{2} + z^{2} = 31 ?$
Option 1: 27
Option 2: 3
Option 3: 54
Option 4: 9