Question

please help me in this question​

Answer 1

Given :

• Evaluate each of the following expression for x=-2 ,y=-1 ,z=3

$\bf \: (1)3 {x}^{2} y + 5x {y}^{2} + 2xyz$

$\\ \bf \: (2) {x}^{3} + {y}^{3} + {z}^{3} - 3xyz$

$\\ \bf \: (3) \: \frac{x}{y} + \frac{y}{z} + \frac{z}{x}$

To Find :

•The remainder from this equation=?

Solution :

•The given values of x =-2 ,y=-1 ,z=3

$\bf \: (1)3 {x}^{2} y + 5x {y}^{2} + 2xyz$

Substituting the values of x, y, and z

$\\ \implies \sf \: 3 {( - 2)}^{2} ( - 1) + 5( - 2) {( - 1)}^{2} + 2( - 2)( - 1)(3)$

$\\ \implies \sf \: 3(4)( - 1) + 5( - 2)(1) + 2(2)(3)$

$\implies \sf \: - 12 + ( - 10) + 12$

$\implies \sf \: - 22 + 12$

$\implies \boxed{ \sf{ - 10}}$

$\bf \: (2) {x}^{3} + {y}^{3} + {z}^{3} - 3xyz$

Substituting the values of x ,y, and z

$\\ \implies \sf {( - 2)}^{3} + {( - 1)}^{3} + {(3)}^{3} + 3( - 2)( - 1)(3)$

$\implies \sf \: - 8 - 1 + 27 + 3(2)(3)$

$\implies \sf \: - 9 + 27 + 18$

$\implies \sf \: 18 + 18 = 36$

$\implies \boxed{ \sf{36}}$

$\\ \bf \: (3) \frac{x}{y} + \frac{y}{z} + \frac{z}{x}$

Substituting the values of x, y, and z

$\\ \implies \sf \: \frac{ - 2}{ - 1} + \frac{ - 1}{3} + \frac{3}{ - 1}$

$\\ \implies \sf \: 2 - \frac{1}{3} - 3$

$\\ \implies \sf \: \frac{6 - 1}{3} - 3$

$\\ \implies \sf \: \frac{5}{3} - 3 = \frac{5 - 9}{3}$

$\implies \boxed{ \sf{ \frac{ - 4}{3}}}$