Question

If x = 1, y = 2 and z = 5, find the value of
(i) 3x − 2y + 4z
(ii) x² + y² + z²
(iii) 2x² − 3y² + z²
(iv) xy + yz − zx
(v) 2x² y − 5yz + xy²
(vi) x³ − y³ − z³

Answer 1

(i) 3x-2y+4z
Substituting x = 1, y = 2 and z = 5 in the given expression:
$$\begin{gathered} 3\times \left(1\right)-2\times \left(2\right)+4\times \left(5\right)=3-4+20 \\ =19 \end{gathered}$$

(ii) ${\mathrm{x}}^2+{\mathrm{y}}^2+{\mathrm{z}}^2$
Substituting x = 1, y = 2 and z = 5 in the given expression:
$$\begin{gathered} 1^2+2^2+5^2=(1\times 1)+(2\times 2)+(5\times 5)=1+4+25 \\ =30 \end{gathered}$$

(iii) $2{\mathrm{x}}^2-3{\mathrm{y}}^2+{\mathrm{z}}^2$
Substituting x = 1, y = 2 and z = 5 in the given expression:
$$\begin{gathered} 2\times (1{)}^2-3\times (2{)}^2+5^2=2\times (1\times 1)-3\times (2\times 2)+(5\times 5)=2-12+25 \\ =15 \end{gathered}$$

(iv) $\mathrm{xy}+\mathrm{yz}-\mathrm{zx}$
Substituting x = 1, y = 2 and z = 5 in the given expression:
$$\begin{gathered} (1\times 2)+(2\times 5)-(5\times 1)=2+10-5 \\ =7 \end{gathered}$$

(v) $2{\mathrm{x}}^2\mathrm{y}-5\mathrm{yz}+{\mathrm{xy}}^2$
Substituting x = 1, y = 2 and z = 5 in the given expression:
$$\begin{gathered} 2\times (1{)}^2\times 2-5\times 2\times 5+1\times (2{)}^2=4-50+4 \\ =-42 \end{gathered}$$

(vi) $x^3-y^3-z^3$
Substituting x = 1, y = 2 and z = 5 in the given expression:
$$\begin{gathered} 1^3-2^3-5^3=(1\times 1\times 1)-(2\times 2\times 2)-(5\times 5\times 5)=1-8-125 \\ =-132 \end{gathered}$$