a+b = do u know
A and B are positive real numbers such that A > B , A 2 + B 2 = 1 3 , A B = 6 . What is A 2 − B 2 ?
The answer is 5.
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5 solutions
A 2 + B 2 = 1 3 A B = 6 So: ( A + B ) 2 = A 2 + B 2 + 2 A B = 1 3 + 2 ( 6 ) = 1 3 + 1 2 = 2 5 → A + B = 5 ( A − B ) 2 = A 2 + B 2 − 2 A B = 1 3 − 1 2 = 1 → A − B = 1 a 2 − B 2 = ( A + B ) ( A − B ) = 5 × 1 = 5
A2 + B2 = 13 AB = 6 A2 + B2 +2AB = (A+B)2 13+12 = (A+B)2 A+B = 5-------------1 A2 + B2 -2AB = (A-B)2 1= (A-B)2 A-B=1------------------2 From 1 and 2 A=3 B=2 SO , A2 - B2 =5
Please note that when you take square roots, there are 2 possible values.
thank you sir for your suggestions.
AxA - BxB =(A+B)(A-B)
Thanks. Those who previously answered -5 have been marked correct.
I have updated the question to state that "A and B are positive reals".
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A^2 + B^2 (=13) + 2(AB)( =2*6 = 12) = 25
or, (A+B)^2 = 25
or, (A+B) = 5
similarly (A-B)=1
Now, (A+B) * (A-B) = A^2 - B^2 = 5*1 =5