第4章 4.25

(1)

x49x2+20=(x25)(x24)=(x5)(x+5)(x2)(x+2)x^4 - 9x^2 + 20 = (x^2-5)(x^2-4) = (x-\sqrt{5})(x+\sqrt{5})(x-2)(x+2)

(2)

x4x26=(x23)(x2+2)=(x3)(x+3)(x2+2)x^4 - x^2 - 6 = (x^2-3)(x^2+2) = (x-\sqrt{3})(x+\sqrt{3})(x^2+2)

(3)

x4+3x2+9=(x2+3)23x2=(x23x+3)(x2+3x+3)x^4 + 3x^2 + 9 = (x^2+3)^2 - 3x^2 = (x^2-\sqrt{3}x+3)(x^2+\sqrt{3}x+3)

(4)

x4+4y4+2x2y2=(x2+2y2)22x2y2=(x22xy+2y2)(x2+2xy+2y2)x^4 + 4y^4 + 2x^2y^2 = (x^2+2y^2)^2 - 2x^2y^2 = (x^2-\sqrt{2}xy+2y^2)(x^2+\sqrt{2}xy+2y^2)

解説: r31bn1z