SOLUTION: find the value for x^2 + y^2 if x + y=7 and x^3 + y^3 = 19

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Question 1140364: find the value for x^2 + y^2 if x + y=7 and x^3 + y^3 = 19
Answer by dkppathak(439) About Me  (Show Source):
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find the value for x^2 + y^2 if x + y=7 and x^3 + y^3 = 19
solution
(x+y)^3=x^3+y^3+3xy(X+Y) by putting x^3 + y^3 = 19
7^3=19+3xy(7)
343=19+21xy
343-19=21xy
324=21xy
324/21=xy
xy=108/7
again
(x+Y)^2=x^2+Y^2+2xy
7^2=X^2+Y^2+2(108/7)
49-216/7=X^2+Y^2
343-216/7=X^2+Y^2
127/7=X^2+Y^2
18.14=x^2+Y^2