Cho (x2 + y2 – 17)2 – 4(xy – 4)2 = (x + y + 5)(x – y + 3)(x + y + m)(x – y + n)

* Hướng dẫn giải

Ta có:

$$\begin{gathered} {\left(x^2+y^2-17\right)}^2-4{\left(xy-4\right)}^2 \\ ={\left(x^2+y^2-17\right)}^2-{\left[2\left(xy-4\right)\right]}^2 \\ =\left(x^2+y^2-17+2xy-8\right)\left(x^2+y^2-17-2xy+8\right) \\ =\left(x^2+y^2+2xy-25\right)\left(x^2+y^2-2xy-9\right) \\ =\left[{\left(x+y\right)}^2-5^2\right]\left[{\left(x-y\right)}^2-3^2\right] \\ =\left(x+y+5\right)\left(x+y-5\right)\left(x-y+3\right)\left(x-y-3\right) \\ \Rightarrow m=-5;n=-3 \Rightarrow m.n=\left(-5\right).\left(-3\right)=15 \end{gathered}$$

Đáp án cần chọn là: D