If a2 + b2 + c2 + 27 = 6(a + b + c), then what is the value of $$\root 3 \of {{a^3} + {b^3} - {c^3}} ?$$
A. 3
B. 1
C. 9
D. 6
Answer: Option A
Solution(By Examveda Team)
$$\eqalign{ & {a^2} + {b^2} + {c^2} + 27 = 6\left( {a + b + c} \right) \cr & {\left( {a - 3} \right)^2} + {\left( {b - 3} \right)^2} + {\left( {c - 3} \right)^2} = 0 \cr & a = 3,\,b = 3,\,c = 3 \cr & \root 3 \of {{a^3} + {b^3} - {c^3}} \cr & = \root 3 \of {27 + 27 - 27} \cr & = \root 3 \of {27} \cr & = 3 \cr} $$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. $$1 + \frac{1}{{x + 4}}$$
B. x + 4
C. $$\frac{1}{x}$$
D. $$\frac{{x + 4}}{x}$$
A. $$\frac{{20}}{{27}}$$
B. $$\frac{{27}}{{20}}$$
C. $$\frac{6}{8}$$
D. $$\frac{8}{6}$$
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