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x^2 + y^2 =9873 ( x + y )^2 = 18225 Find ( x^3 + y^3 )/45
The answer is 17091.
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1 solution
x^2 + y^2 =9873. ( x + y )^2 = 18225 implies x+y=135. implies, x^2 + y^2+2xy=18225. that implies 2xy=18225-9873. thus,xy=4176. moreover, (x^3+y^3)/45=(x+y)(x^2+y^2-xy)/45. =135/45 x (9873-4176). =3 x (5397). =17091.