Polynomials.. -_-

Algebra Level 2

Given that $a - b = 2$ and $c - b = 3$ , find the value of

$a^2 + b^2 + c^2 - ab - bc - ac.$

2 solutions

Christian Daang
Oct 26, 2014

given: a-b = 2 (i) and c-b = 3 (ii)

c-a = 1 (iii)

then, the given equation is equal to:

[(i)^2 + (ii)^2 + (iii)^2]/2

= [2^2 + 3^2 + 1^2]/2

= {4+9+1]/2

= 7

Final answer: 7

William Isoroku
Dec 28, 2014

Set the equations to $a=2+b$ and $c=3+b$ and substitute those values of $a$ and $b$ into the equation that we're trying to solve.

Helpful note: $a^2+b^2+c^2-ab-cb-ac=(a+b+c)^2-3(ab+bc+ac)$

Then all the variables cancel out and left with a number, which is $\boxed{7}$