If x + y + z = 19, xy + yz + zx = 144, then the value of $$\sqrt {{x^3} + {y^3} + {z^3} - 3xyz} $$ is:
A. 21
B. 17
C. 19
D. 13
Answer: Option C
Solution(By Examveda Team)
$$\eqalign{ & x + y + z = 19, \cr & xy + yz + zx = 144, \cr & \sqrt {{x^3} + {y^3} + {z^3} - 3xyz} \cr & {\text{Let }}z = 0 \cr & x + y = 19,\,xy = 144,\,\sqrt {{x^3} + {y^3}} = ? \cr & \sqrt {{x^3} + {y^3}} \cr & = \sqrt {\left( {x + y} \right)\left[ {{{\left( {x + y} \right)}^2} - 3xy} \right]} \cr & = \sqrt {19\left( {{{19}^2} - 3 \times 144} \right)} \cr & = \sqrt {19 \times 19} \cr & = 19 \cr} $$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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