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?
A. 6
B. 9
C. 0
D. 1
Answer: Option C
Solution(By Examveda Team)
$$\eqalign{ & \mathop {\mathop {{{\left( {x - 4} \right)}^3}}\limits_ \Downarrow }\limits_{{a^3}} + \mathop {\mathop {{{\left( {y - 2} \right)}^3}}\limits_ \Downarrow }\limits_{{b^3}} + \mathop {\mathop {{{\left( {z - 3} \right)}^3}}\limits_ \Downarrow }\limits_{{c^3} - 3abc} - 3\left( {x - 4} \right)\left( {y - 2} \right)\left( {z - 3} \right) \cr & \Rightarrow a + b + c = x - 4 + y - 2 + z - 3 \cr & \Rightarrow a + b + c = x + y + z - 9 \cr & \Rightarrow a + b + c = 9 - 9 \cr & \Rightarrow a + b + c = 0 \cr} $$$${\text{So, }}{\left( {x - 4} \right)^3} + {\left( {y - 2} \right)^3} + $$ $${\left( {z - 3} \right)^3} - $$ $$3\left( {x - 4} \right)$$ $$\left( {y - 2} \right)$$ $$\left( {z - 3} \right)$$
$$ \Rightarrow 0$$
Related Questions on Algebra
If $$p \times q = p + q + \frac{p}{q}{\text{,}}$$ then the value of 8 × 2 is?
A. 6
B. 10
C. 14
D. 16
A. $$1 + \frac{1}{{x + 4}}$$
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C. $$\frac{1}{x}$$
D. $$\frac{{x + 4}}{x}$$
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B. $$\frac{{27}}{{20}}$$
C. $$\frac{6}{8}$$
D. $$\frac{8}{6}$$
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