x + y = 5
(x + y)2 = 52
x2 + 2xy + y2 = 25 (*)
Thay xy = - 0,5 vào (*), ta có:
x2 + 2 . (- 0,5) + y2 = 25
x2 + y2 - 1 = 25
x2 + y2 = 25 + 1
x2 + y2 = 26
\(P=\frac{\left(\frac{x^2}{x^2-y^2}+\frac{y}{x-y}\right)}{\left(\frac{x^3-y^3}{x^5-x^4y-xy^4+y^5}\right)}\)
\(=\frac{\left(\frac{x^2+xy+y^2}{x^2-y^2}\right)}{\left(\frac{\left(x-y\right)\left(x^2+xy+y^2\right)}{\left(x-y\right)\left(x^2-y^2\right)\left(x^2+y^2\right)}\right)}\)
\(=\frac{\left(x^2+xy+y^2\right)}{\left(x^2-y^2\right)}\times\frac{\left(x-y\right)\left(x^2-y^2\right)\left(x^2+y^2\right)}{\left(x-y\right)\left(x^2+xy+y^2\right)}\)
\(=x^2+y^2\)
= 26
ĐS: 26
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