Three unknowns

Algebra Level 4

2 a + 3 b + 4 c = 48. 2a+3b+4c=48.
6 a 7 c 2 b = 39. 6a-7c-2b=-39.
3 c 2 a b = 3. 3c-2a-b=3.
a 2 + b 2 + c 2 = d . a^2+b^2+c^2=d.
Find the value of d 2 d^2 .


The answer is 8649.

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1 solution

Jack Sacks
Feb 13, 2016

3c-2a-b =3 therefore b=3c-2a-3.
Substituting this into the first two equations we obtain:
10a-13c=-45.
And -4a+13c=57
Adding these equations together we obtain:
6a=12 therefore a=2. Substituting this back into 10a-13c=45 we discover that c=5
Substituting c=5 and a=2 back into one of the original equations we obtain b=8
8^2+5^2+2^2=93
93^2=8649


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