If x = 2015, y = 2014, z = 2013, then the value of x2 + y2 + z2 - xy - yz - zx is?
A. 3
B. 4
C. 6
D. 2
Answer: Option A
Solution(By Examveda Team)
$$\eqalign{ & x = 2015 \cr & y = 2014 \cr & z = 2013 \cr & \therefore {x^2} + {y^2} + {z^2} - xy - yz - zx \cr & = \frac{1}{2}\left[ {{{\left( {x - y} \right)}^2} + {{\left( {y - z} \right)}^2} + {{\left( {z - x} \right)}^2}} \right] \cr & = \frac{1}{2}\left[ {{{\left( {2015 - 2014} \right)}^2} + {{\left( {2014 - 2013} \right)}^2} + {{\left( {2013 - 2015} \right)}^2}} \right] \cr & = \frac{1}{2}\left( {1 + 1 + 4} \right) \cr & = 3 \cr} $$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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