Absolute Difference

Algebra Level 3

Given that $a , b , c \in \mathbb{Z}$ and $a>10$ and
$(x-a)(x-12)+2=(x+b)(x+c)$
Find the value of $\left | b-c \right |$

The answer is 1.

2 solutions

Bill Bell
Sep 19, 2014

Using the Python sympy library one can expand the product on the right of the equation and try successive values of 'a' beginning with 11 to see which is the first to yield a quadratic that can be factored:

from sympy import *
x,a,b,c = symbols ( 'x a b c')

exp = ((x-a)*(x-12)+2).expand()
val = 10
while True :
    val += 1
    exp_eval = exp . subs ( a, val )
    factors = factor ( exp_eval )
    if not exp_eval == factors :
        print val, factors
        break

This code prints : 15 (x - 14)*(x - 13)

Akshitha Ganji
Jun 6, 2014

we can commonly say that they say that a is greater than 10 and the number is 11 so 12-11=1

Absolute Difference

The answer is 1.

2 solutions

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