SOLUTION: Find a^2+b^2+c^2 If a+b=c+6 and ab-ac=bc-1 please help me to solve this kind of math problem I am really eager to know how to solve it . I just know that the answer is 38 But how ?

Question 935704: Find a^2+b^2+c^2 If a+b=c+6 and ab-ac=bc-1 please help me to solve this kind of math problem I am really eager to know how to solve it . I just know that the answer is 38 But how ? Thank you in advance
Found 2 solutions by jim_thompson5910, josgarithmetic:
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Focus on the second equation and get all the variable terms to one side

ab-ac=bc-1

ab-ac-bc=-1 equation 1

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Move onto the second equation, subtract c from both sides, and square both sides
Do a bit more work and isolate a^2+b^2+c^2 like so...

a+b=c+6

a+b-c=6

(a+b-c)^2=6^2

(a+b-c)(a+b-c)=36

a(a+b-c)+b(a+b-c)-c(a+b-c)=36

a^2+ab-ac+ab+b^2-bc-ac-bc+c^2=36

a^2+b^2+c^2+ab-ac+ab-bc-ac-bc=36

a^2+b^2+c^2+2ab-2ac-2bc=36

a^2+b^2+c^2+2(ab-ac-bc)=36

a^2+b^2+c^2+2(-1)=36 ... replace ab-ac-bc with -1 (see equation 1)

a^2+b^2+c^2-2=36

a^2+b^2+c^2=36+2

a^2+b^2+c^2=38
Answer by josgarithmetic(39617) (Show Source): You can put this solution on YOUR website!
You must be missing some information. The description gives one expression in three variables, and two equations in the same three variables. You can eliminate any ONE variable using the two equations, and you will then have one equation in TWO variables and the same expression in THREE variables. The expression has not yet a value. To say you know the answer is 38 depends on information not given, and the information is needed before you can find the value.
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