If a + b + c = 10 ; $a^2 + b^2 + c^2 = 38$, what is the value of $(a − b)^2 + (b − c)^2 + (c − a)^2$?
Answer & explanation
Correct answer: option 3
If a + b + c = 10 ; $a^2 + b^2 + c^2 = 38$
what is the value of $(a − b)^2 + (b − c)^2 + (c − a)^2$
If the number of equations are less than the number of variables then we can put the extra variables according to our choice =
So here two equations given and three variables are present so put c = 0
If a + b = 10
$a^2 + b^2 = 38$
then,
( a + b )2 = a2 + b2 + 2ab
(10 )2 = 38 + 2ab
2ab = 62
ab = 31
$(a − b)^2 + (b )^2 + (− a)^2$ = a2 + b2 - 2ab + b2 + a2
= 38 + 38 -2 × 31
= 76 - 62 = 14