SOLUTION: If a+b=2 and b*a= −1, then a^2 + b^2 = (A)4 (B)5 (C)6 (D)8 (E)10

Algebra ->  Complex Numbers Imaginary Numbers Solvers and Lesson -> SOLUTION: If a+b=2 and b*a= −1, then a^2 + b^2 = (A)4 (B)5 (C)6 (D)8 (E)10       Log On


   

Question 1149697: If a+b=2 and b*a= −1, then a^2 + b^2 =
(A)4
(B)5
(C)6
(D)8
(E)10
Found 2 solutions by Alan3354, ikleyn:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
If a+b=2 and b*a= −1, then a^2 + b^2 =
(A)4
(B)5
(C)6
(D)8
(E)10
================
With only 5 to choose from, try each one.

Answer by ikleyn(52780) About Me  (Show Source):
You can put this solution on YOUR website!
.

Since a + b = 2, square both sides to get


    (a + b)^2 = 4

    a^2 + 2ab + b^2 = 4


Next, replace ab by -1, since it is given.  You will get


    a^2 -2 + b^2 = 4,


which implies


    a^2 + b^2 = 4 + 2 = 6.


ANSWER.  Under the given conditions,  a^2 + b^2 = 6.

Solved.


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Comment from student:  Thanks a lot Ikleyn.  What is the link of your website?  I can share.
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If you really want to get the response from me to your message/"comment",
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