簡約 sqrt((3-3x^2)^2+(6x)^2)

解

簡約

(3 - 3 x^{2})^{2} + (6 x)^{2}

3 x^{2} + 3

解答ステップ

(3 - 3 x^{2})^{2} + (6 x)^{2}

簡素化

(3 - 3 x^{2})^{2} + (6 x)^{2} : 9 x^{4} + 18 x^{2} + 9

= 9 x^{4} + 18 x^{2} + 9

共通項をくくり出す

9 : 9 (x^{4} + 2 x^{2} + 1)

= 9 (x^{4} + 2 x^{2} + 1)

累乗根の規則を適用する:

ab = a b,

, 以下を想定

a \geq 0, b \geq 0

9 (x^{4} + 2 x^{2} + 1) = 9 x^{4} + 2 x^{2} + 1

= 9 x^{4} + 2 x^{2} + 1

9 = 3

= 3 x^{4} + 2 x^{2} + 1

簡素化

x^{4} + 2 x^{2} + 1 : x^{2} + 1

= 3 (x^{2} + 1)

拡張

3 (x^{2} + 1) : 3 x^{2} + 3

= 3 x^{2} + 3