If a = 7, b = 5 and c = 3, then the value of a2 + b2 + c2 - ab - bc - ca is?
A. 12
B. -12
C. 0
D. 8
Answer: Option A
Solution(By Examveda Team)
$$\eqalign{ & {a^2} + {b^2} + {c^2} - ab - bc - ca \cr & = \frac{1}{2}\left[ {{{\left( {a - b} \right)}^2} + {{\left( {b - c} \right)}^2} + {{\left( {c - a} \right)}^2}} \right] \cr & = \frac{1}{2}\left[ {{{\left( {7 - 5} \right)}^2} + {{\left( {5 - 3} \right)}^2} + {{\left( {3 - 7} \right)}^2}} \right] \cr & = \frac{1}{2}\left( {4 + 4 + 16} \right) \cr & = \frac{{24}}{2} \cr & = 12 \cr} $$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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