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人気のある代数 >

(6x^2)/((sqrt(2x+1)+1)^2)=2x+sqrt(x-1)+1

解

\frac{6 x ^{2}}{( 2 x + 1 + 1 ) ^{2}} = 2 x + x - 1 + 1

解

x = 23.56067 \dots

解答ステップ

\frac{6 x ^{2}}{( 2 x + 1 + 1 ) ^{2}} = 2 x + x - 1 + 1

以下で両辺を乗じる:

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

\frac{6 x ^{2}}{( 2 x + 1 + 1 ) ^{2}} (2 x + 1 + 1)^{2} = 2 x (2 x + 1 + 1)^{2} + x - 1 (2 x + 1 + 1)^{2} + 1 \cdot (2 x + 1 + 1)^{2}

簡素化

6 x^{2} = 2 x (2 x + 1 + 1)^{2} + x - 1 (2 x + 1 + 1)^{2} + (2 x + 1 + 1)^{2}

拡張

2 x (2 x + 1 + 1)^{2} + x - 1 (2 x + 1 + 1)^{2} + (2 x + 1 + 1)^{2} : 4 x^{2} + 6 x + 4 x 2 x + 1 + 2 x x - 1 + 2 x - 1 + 2 x - 1 2 x + 1 + 2 2 x + 1 + 2

6 x^{2} = 4 x^{2} + 6 x + 4 x 2 x + 1 + 2 x x - 1 + 2 x - 1 + 2 x - 1 2 x + 1 + 2 2 x + 1 + 2

equationを

x - 1 = u

と以下で書き換える:

x = u^{2} + 1

6 (u^{2} + 1)^{2} = 4 (u^{2} + 1)^{2} + 6 (u^{2} + 1) + 4 (u^{2} + 1) 2 (u^{2} + 1) + 1 + 2 (u^{2} + 1) u + 2 u + 2 u 2 (u^{2} + 1) + 1 + 2 2 (u^{2} + 1) + 1 + 2

解く

6 (u^{2} + 1)^{2} = 4 (u^{2} + 1)^{2} + 6 (u^{2} + 1) + 4 (u^{2} + 1) 2 (u^{2} + 1) + 1 + 2 (u^{2} + 1) u + 2 u + 2 u 2 (u^{2} + 1) + 1 + 2 2 (u^{2} + 1) + 1 + 2 : u \approx - 2.52756 \dots, u \approx 4.74980 \dots

u \approx - 2.52756 \dots, u \approx 4.74980 \dots

再び

u = x - 1

に置き換えて以下を解く:

x

解く

x - 1 = - 2.52756 \dots :

以下の解はない:

x \in R

解く

x - 1 = 4.74980 \dots : x = 23.56067 \dots

x = 23.56067 \dots

解を検算する:

x = 23.56067 \dots

真

解は

x = 23.56067 \dots

グラフ

人気の例

c= 1/((sqrt(x^2+x-2)))

c = \frac{1}{( x ^{2} + x - 2 )}

2x^2+2sqrt(5x)-5=0

2 x^{2} + 2 5 x - 5 = 0

((x-1)/x)^{1/2}+((1-1)/x)^{1/2}=x

(\frac{x - 1}{x})^{\frac{1}{2}} + (\frac{1 - 1}{x})^{\frac{1}{2}} = x

sqrt(x+1)+sqrt(2x+3)=5

x + 1 + 2 x + 3 = 5

2 x - 3 = - 1