SOLUTION: If a+c=-8 and c-b=-4, find the value of {{{3a^2-6b^20+3c^2}}}. CC11F #3

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Question 1209407: If a+c=-8 and c-b=-4, find the value of 3a%5E2-6b%5E20%2B3c%5E2.
CC11F #3
Found 2 solutions by greenestamps, ikleyn:
Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


The problem is clearly stated incorrectly.

The given information makes it easy to find parametric expressions for a, b, and c; and virtually any two sets of values for a, b, and c derived using those parametric equations will result in different values for the given expression.

Answer by ikleyn(52782) About Me  (Show Source):
You can put this solution on YOUR website!
.
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If a+c=-8 and c-b=-4, find the value of 3a%5E2-6b%5E20%2B3c%5E2.
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      My interior voice tells me that the correct problem is THIS

                If   a + c = -8   and   c - b = -4,   find the value of   3a%5E2-6b%5E2%2B3c%5E2.         (*)

        I will solve in this formulation 


We have 

    a + c = -8,    (1)

    c - b = -4.    (2)



Subtract eq(2) from eq(1).  You will get

    a + b = -4     (3)


Now 

    3a%5E2+-+6b%5E2+%2B+c%5E2 = 3%2A%28%28a%5E2-b%5E2%29-%28b%5E2-c%5E2%29%29 = (3*(a-b)*(a+b)-(b-c)*(b+c)) = 


            here replace  (a+b)  by -4 based on (3);  replace  (b-c) by 4  based on (2),  and continue


    = 3*((a-b)*(-4) - 4*(b+c)) = 3*4(b-a)-(b+c)) = 12*(-a-c) = 


            here replace (-a-c)  by 8,  based on (1),  and continue


    = 12*8 = 96.


ANSWER.  After simplifications, the value of  (*)  is  96.

Solved.