INTKILOW
commented
1 year ago 首先计算出 $7m^2-14m = 7(1+\sqrt{2})^2 - 14(1+\sqrt{2}) = -7\sqrt{2}$，$3n^2-6n-7 = 3(1-\sqrt{2})^2-6(1-\sqrt{2})-7 = -7\sqrt{2}$。因此 $(7m^2-14m+a)(3n^2-6n-7) = (-7\sqrt{2}+a)(-7\sqrt{2})=8$。解得 $a = \frac{8}{7\sqrt{2}}-7\sqrt{2} = -\frac{37}{7}\sqrt{2}$。所以 $a=-\frac{37}{7}\sqrt{2}$。
sbfkcel
首先计算出 $7m^2-14m = 7(1+\sqrt{2})^2 - 14(1+\sqrt{2}) = -7\sqrt{2}$，$3n^2-6n-7 = 3(1-\sqrt{2})^2-6(1-\sqrt{2})-7 = -7\sqrt{2}$。因此 $(7m^2-14m+a)(3n^2-6n-7) = (-7\sqrt{2}+a)(-7\sqrt{2})=8$。解得 $a = \frac{8}{7\sqrt{2}}-7\sqrt{2} = -\frac{37}{7}\sqrt{2}$。所以 $a=-\frac{37}{7}\sqrt{2}$。