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 Suppose that $ab = 7$ and $a^2b + ab^2 + a+b = 80$. What is $a^2+b^2$? 

 Sep 25, 2017
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ab  = 7

a^2b + ab^2  + a + b  = 80

 

What  is     a^2 + b^2   ???

 

So we have :

 

a^2b + ab^2  + a + b  = 80         factor  the first two terms

 

ab (a + b)  + (a + b)  = 80        factor again

 

( a + b) (ab + 1)  = 80

 

(a + b) (7 + 1)  = 80

 

(a + b) (8)  = 80     divide by 8 on both sides

 

a + b  =   10

 

Square both sides

 

a^2 + 2ab + b^2  = 100

 

a^2 + 2(7) + b^2   = 100 

 

a^2 + 14 + b^2   = 100       subtract 14 from both sides

 

a^2 + b^2   =  86

 

 

cool cool cool

 Sep 25, 2017

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