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

Guest Jan 31, 2015

Best Answer 

 #1
avatar+92565 
+6

ab = 7

a^2b + ab^2 + a + b = 80     factor

a(ab + 1) + b(ab + 1) = 80

(a + b)(ab + 1) = 80

(a+b)(7 + 1) = 80

a + b = 80/8

a + b = 10      square both sides

a^2 + 2ab + b^2 = 100

a^2 +2(7) + b^2 = 100

a^2 + 14 + b2 = 100

a^2 + b^2 = 86

 

CPhill  Jan 31, 2015
 #1
avatar+92565 
+6
Best Answer

ab = 7

a^2b + ab^2 + a + b = 80     factor

a(ab + 1) + b(ab + 1) = 80

(a + b)(ab + 1) = 80

(a+b)(7 + 1) = 80

a + b = 80/8

a + b = 10      square both sides

a^2 + 2ab + b^2 = 100

a^2 +2(7) + b^2 = 100

a^2 + 14 + b2 = 100

a^2 + b^2 = 86

 

CPhill  Jan 31, 2015

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