If x + y + z = 6 and x2 + y2 + z2 = 20, then the value of x3 + y3 + z3 - 3xyz is?
A. 64
B. 70
C. 72
D. 76
Answer: Option C
Solution(By Examveda Team)
$$\eqalign{ & x + y + z = 6 \cr & {x^2} + {y^2} + {z^2} = 20 \cr & \Rightarrow {\left( {x + y + z} \right)^2} = {\left( 6 \right)^2} \cr & \Rightarrow {x^2} + {y^2} + {z^2} + 2\left( {xy + yz + zx} \right) = 36 \cr & \Rightarrow 20 + 2\left( {xy + yz + zx} \right) = 36 \cr & \Rightarrow 2\left( {xy + yz + zx} \right) = 16 \cr & \Rightarrow xy + yz + zx = 8 \cr & \therefore {\text{ }}{x^3} + {y^3} + {z^3} - 3xyz \cr & = \left( {x + y + z} \right)\left( {{\text{ }}{x^2} + {y^2} + {z^2} - xy - zx - yz} \right) \cr & = {x^3} + {y^3} + {z^3} - 3xyz = 6\left( {20 - 8} \right) \cr & = 6\left( {20 - 8} \right) \cr & = 6 \times 12 \cr & = 72 \cr} $$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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