Find the Value
\[ 4x^2 + y^2 + 25z^2 + 4xy – 10yz – 20zx \]
Given:
\[ x=4,\quad y=3,\quad z=2 \]
Solution:
Using identity:
\[ (a+b-c)^2 = a^2+b^2+c^2+2ab-2bc-2ca \]
\[ 4x^2 + y^2 + 25z^2 + 4xy – 10yz – 20zx \]
\[ = (2x)^2 + y^2 + (5z)^2 +2(2x)(y) -2(y)(5z) -2(2x)(5z) \]
\[ = (2x+y-5z)^2 \]
\[ = (2(4)+3-5(2))^2 \]
\[ = (8+3-10)^2 \]
\[ = (1)^2 \]
\[ =1 \]