Question : If $x + y + z = 9$ , then the value of $(x - 4)^{3} + (y - 2)^{3} + (z - 3)^{3} - 3 (x - 4) (y - 2) (z - 3)$ is:
Option 1: 6
Option 2: 9
Option 3: 0
Option 4: 1

Question

Question : If $x + y + z = 0$ , then what is the value of $\frac{x^{2}}{(y z)} + \frac{y^{2}}{(x z)} + \frac{z^{2}}{(x y)}$ ?

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Answer 1

Correct Answer: 0

Solution : Given: $x + y + z = 9$
Solution:
Let $(x - 4) = a, (y - 2) = b, (z - 3) = c$
So, this equation stands to
$ (x - 4)^{3} + (y - 2)^{3} + (z - 3)^{3} - 3 (x - 4) (y - 2) (z - 3)$
= $a^{3} + b^{3} + c^{3} - 3 a b c$
Also, We know that $a^{3} + b^{3} + c^{3} - 3 a b c$ = $(a + b + c) (a^{2} + b^{2} + c^{2} - b c - a b - a c)$ .
So, $a + b + c = x - 4 + y - 2 + z - 3$
⇒ $a + b + c = x + y + z - 9$
⇒ $a + b + c = 9 - 9$
⇒ $a + b + c = 0$
So, $(x - 4)^{3} + (y - 2)^{3} + (z - 3)^{3} - 3 (x - 4) (y - 2) (z - 3) = 0$
Hence, the correct answer is 0.

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Question : If x+y+z=9, then the value of (x−4)3+(y−2)3+(z−3)3−3(x−4)(y−2)(z−3) is:Option 1: 6Option 2: 9Option 3: 0Option 4: 1

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Question : If $x + y + z = 9$ , then the value of $(x - 4)^{3} + (y - 2)^{3} + (z - 3)^{3} - 3 (x - 4) (y - 2) (z - 3)$ is:
Option 1: 6
Option 2: 9
Option 3: 0
Option 4: 1