Given $$ a+b+2c=1 $$ , $$ a^2+b^2-8c^2+6c=5 $$ , find the value of $$ ab-bc-ca $$ .

Question

Given $$ a+b+2c=1 $$ , $$ a^2+b^2-8c^2+6c=5 $$ , find the value of  $$ ab-bc-ca $$ .

Uniteasy Admin · Accepted Answer

$$ a+b+2c=1 $$ 
$$ (a+b)^2=(1-2c)^2 $$
$$ a^2+b^2+2ab=4c^2-4c+1 $$n
$$ a^2+b^2-8c^2+6c=5 $$n
Subtract expressions: (1) - (2) , we get,
$$ 2ab = -4c^2+2c-4 $$
$$ ab=-2c^2+c-2 $$
$$ 	herefore  ab-bc-ca $$
$$ =-2c^2+c-2 - c(a+b) $$
$$ =-2c^2+c-2 - c(1-2c) $$
$$ =-2c^2+c-2 - c+2c^2 $$
$$ =-2 $$

Question

Answer