Question 1022705: please help me out my problem is:
If a+2b=9 and ab=7 than what is the value of aČ+4b?
Found 2 solutions by Edwin McCravy, Theo:
Answer by Edwin McCravy(20060)   (Show Source):
You can put this solution on YOUR website!
Solve a+2b = 9 for a, get a = 9-2b
Square both sides of
a+2b = 9
Substitute ab=7 for ab, and (9-2b) for a
Simplify, get 0 on the right side.
You get a quadratic equation in b that you
can divide thru by 4.
Simplify
The quadratic equation is factorable
You get 2 solutions for b
Substitute each in a = 9-2b to find two solutions for a
Substitute the values of a and b in
aČ+4b, and get 2 solutions.
Edwin
Answer by Theo(13342)  (Show Source):
You can put this solution on YOUR website! If a + 2b = 9 and ab = 7 than what is the value of a^2 + 4b?
you have a + 2b = 9 and you have ab = 7.
solve for a in ab = 7 to get a = 7/b.
a + 2b = 9 becomes 7/b + 2b = 9 after you replace a with 7/b.
your equation to solve is now 7/b + 2b = 9.
multiply both sides of that equation by b to get 7 + 2b^2 = 9b.
subtract 9b from both sides of the equation and reorder the terms in descending order to get 2b^2 - 9b + 7 = 0
factor that quadratic to get (2b-7) * (b-1) = 0
solve for b to get b = 7/2 or b = 1.
when b = 7/2, a + 2b = 9 becomes a + 7 = 9 which becomes a = 2.
when b = 1, a + 2b = 9 becomes a + 2 = 9 which becomes a = 7.
you have two possibilities.
a = 2 and b = 7/2.
a = 7 and b = 1.
when a = 2 and b = 7/2, a + 2b = 9 becomes 2 + 7 = 9 which becomes 9 = 9 which is true.
when a = 2 and b = 7/2 ab = 7 becomes 2 * 7/2 = 7 which becomes 7 = 7 which is true.
when a = 7 and b = 1, a + 2b = 9 becomes 7 + 2 = 9 which becomes 9 = 9 which is true.
when a = 7 and b = 1, ab = 7 becomes 7 * 1 = 7 which becomes 7 = 7 which is true.
the above 4 equations confirm the solutions are correct so far.
so we have two pairs of solutions in the form of (a,b).
the are (2,7/2) and (7,1).
now we look at a^2 + 4b.
when a = 2 and b = 7/2, a^2 + 4b = 4 + 14 = 18.
when a = 7 and b = 1, a^2 + 4b = 49 + 4 = 53.
you have 2 solutions.
a^2 + 4b = 18 when a = 2 and b = 7/2.
a^2 + 4b = 53 when a = 7 and b = 1.
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