6 6
a²+b^2
25.
ab = 12 find a+b.
Answers
Answer:
How do you solve A²+B²=25, AB=12, then A+BA−B = ?
Become a Data Scientist at the INSOFE School of Data Science.
Whenever A2+B2 and AB in the same problem, more likely than not we will have to use the identities (A+B)2=A2+2AB+B2 and (A−B)2=A2−2AB+B2 . If you are unfamiliar with these, I encourage you to multiply out the left-hand sides.
From here, the way forward is clear. Using the given values of A2+B2 and AB ,
(A+B)2=A2+B2+2AB=25+24=49 and
(A−B)2=A2+B2−2AB=25−24=1 , so
(A+BA−B)2=49/1=49.
To finish, simply square root both sides (and don’t forget the plus-minus!) to get
A+BA−B=±7.
It turns out that, for this specific problem, the values of A and B are very nice. If you were to solve this by actually finding those values, you would get (A,B)=(3,4),(4,3),(−3,−4),(−4,−3) , and by plugging these pairs into the given expression, you would get the same solution of ±7 .