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Evaluate the expression: a+b−c=7 and ab=bc+ac. Find the value of a+b+c.

a) 5
b) 7
c) 10
d) 12

User Ali Gajani
by
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1 Answer

3 votes

Final answer:

To find the values of a, b, and c, we need to solve the given equations. However, the given values of a, b, and c do not satisfy the second equation, so we cannot find the value of a + b + c.

Step-by-step explanation:

To find the values of a, b, and c, we need to solve the given equations. From the first equation, a + b - c = 7, we can rearrange it as a + b = 7 + c. Substituting this into the second equation, ab = bc + ac, we get (7 + c)b = bc + ac. Expanding and simplifying, we have 7b + cb = bc + ac. Rearranging this equation, we get cb - bc = ac - 7b. Factoring out the common factor on both sides gives (c - b)b = a(c - 7). Therefore, a = b and c - 7 = b. Substituting b for a in the first equation, we have b + b = 7 + c, which simplifies to 2b = 7 + c. Solving this equation simultaneously with c - 7 = b, we can find the values of a, b, and c. However, the given values of a, b, and c do not satisfy the second equation, ab = bc + ac, so we cannot find the value of a + b + c. Therefore, the answer is none of the above (option e).

User Daniel Haughton
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