簡約 (sqrt(x^2+x-2)+sqrt((3-x)(x+2)))^2

解

簡約

(x^{2} + x - 2 + (3 - x) (x + 2))^{2}

2 x + 2 (3 - x) (x + 2) x^{2} + x - 2 + 4

解答ステップ

(x^{2} + x - 2 + (3 - x) (x + 2))^{2}

完全平方式を適用する:

(a + b)^{2} = a^{2} + 2 ab + b^{2}

(x^{2} + x - 2 + (3 - x) (x + 2))^{2} = (x^{2} + x - 2)^{2} + 2 x^{2} + x - 2 (3 - x) (x + 2) + ((3 - x) (x + 2))^{2}

= (x^{2} + x - 2)^{2} + 2 x^{2} + x - 2 (3 - x) (x + 2) + ((3 - x) (x + 2))^{2}

簡素化

(x^{2} + x - 2)^{2} + 2 x^{2} + x - 2 (3 - x) (x + 2) + ((3 - x) (x + 2))^{2} : 2 x + 2 (3 - x) (x + 2) x^{2} + x - 2 + 4

= 2 x + 2 (3 - x) (x + 2) x^{2} + x - 2 + 4