簡約 sqrt(((5-120x)^2+(150x)^2))

解

簡約

((5 - 120 x)^{2} + (150 x)^{2})

5 1 - 48 x + 1476 x^{2}

解答ステップ

(5 - 120 x)^{2} + (150 x)^{2}

規則を適用する:

(a) = a

((5 - 120 x)^{2} + (150 x)^{2}) = (5 - 120 x)^{2} + (150 x)^{2}

= (5 - 120 x)^{2} + (150 x)^{2}

簡素化

(5 - 120 x)^{2} + (150 x)^{2} : 25 - 1200 x + 36900 x^{2}

= 25 - 1200 x + 36900 x^{2}

共通項をくくり出す

25 : 25 (1 - 48 x + 1476 x^{2})

= 25 (1 - 48 x + 1476 x^{2})

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

25 (1 - 48 x + 1476 x^{2}) = 25 1 - 48 x + 1476 x^{2}

= 25 1 - 48 x + 1476 x^{2}

25 = 5

= 5 1 - 48 x + 1476 x^{2}