What is the possible value of ( a + b + c) - 3, if $a^2 + b^2 + c^2= 9$ and ab + bc + ca = 8 ?
Answer & explanation
Correct answer: option 4
If $a^2 + b^2 + c^2= 9$ and ab + bc + ca = 8
If the number of variables is more than the number of equations then we can put extra variables according to our choice.
Here the number of variables are 3 and the number of equations are 2 so, we can put c = 0. we get,
$a^2 + b^2 = 9$
ab = 8
( a + b )2 = a2 + b2 + 2ab
( a + b )2 = 9+ 2 × 8 = 25
a + b = 5
Put the values in ( a + b + c) - 3
( 5 + 0) - 3 = 2