ja

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

人気のある代数 >

((sqrt(x-1)-b-c))/a+((sqrt(x-1)-c-a))/b+((sqrt(x-1)-a-b))/c =3

解

\frac{( x - 1 - b - c )}{a} + \frac{( x - 1 - c - a )}{b} + \frac{( x - 1 - a - b )}{c} = 3

解

x = \frac{( 3 b c a + b ^{2} c + b c ^{2} + c ^{2} a + c a ^{2} + b a ^{2} + b ^{2} a ) ^{2}}{b ^{2} c ^{2} + 2 b c ^{2} a + 2 b ^{2} c a + 2 b c a ^{2} + b ^{2} a ^{2} + c ^{2} a ^{2}} + 1

解答ステップ

\frac{( x - 1 - b - c )}{a} + \frac{( x - 1 - c - a )}{b} + \frac{( x - 1 - a - b )}{c} = 3

以下の最小公倍数を求める:

a, b, c : b c a

以下で乗じる: LCM=

b c a

\frac{x - 1 - b - c}{a} b c a + \frac{x - 1 - c - a}{b} b c a + \frac{x - 1 - a - b}{c} b c a = 3 b c a

簡素化

b c (x - 1 - b - c) + c a (x - 1 - c - a) + ba (x - 1 - a - b) = 3 b c a

拡張

b c (x - 1 - b - c) + c a (x - 1 - c - a) + ba (x - 1 - a - b) : b c x - 1 - b^{2} c - b c^{2} + c a x - 1 - c^{2} a - c a^{2} + ba x - 1 - b a^{2} - b^{2} a

b c x - 1 - b^{2} c - b c^{2} + c a x - 1 - c^{2} a - c a^{2} + ba x - 1 - b a^{2} - b^{2} a = 3 b c a

b^{2} c

を右側に移動します

b c x - 1 - b c^{2} + c a x - 1 - c^{2} a - c a^{2} + ba x - 1 - b a^{2} - b^{2} a = 3 b c a + b^{2} c

b c^{2}

を右側に移動します

b c x - 1 + c a x - 1 - c^{2} a - c a^{2} + ba x - 1 - b a^{2} - b^{2} a = 3 b c a + b^{2} c + b c^{2}

c^{2} a

を右側に移動します

b c x - 1 + c a x - 1 - c a^{2} + ba x - 1 - b a^{2} - b^{2} a = 3 b c a + b^{2} c + b c^{2} + c^{2} a

c a^{2}

を右側に移動します

b c x - 1 + c a x - 1 + ba x - 1 - b a^{2} - b^{2} a = 3 b c a + b^{2} c + b c^{2} + c^{2} a + c a^{2}

b a^{2}

を右側に移動します

b c x - 1 + c a x - 1 + ba x - 1 - b^{2} a = 3 b c a + b^{2} c + b c^{2} + c^{2} a + c a^{2} + b a^{2}

b^{2} a

を右側に移動します

b c x - 1 + c a x - 1 + ba x - 1 = 3 b c a + b^{2} c + b c^{2} + c^{2} a + c a^{2} + b a^{2} + b^{2} a

因数

b c x - 1 + c a x - 1 + ba x - 1 : x - 1 (b c + c a + ba)

x - 1 (b c + c a + ba) = 3 b c a + b^{2} c + b c^{2} + c^{2} a + c a^{2} + b a^{2} + b^{2} a

以下で両辺を割る

b c + c a + ba

x - 1 = \frac{3 b c a + b ^{2} c + b c ^{2} + c ^{2} a + c a ^{2} + b a ^{2} + b ^{2} a}{b c + c a + ba}

両辺を2乗する:

x - 1 = \frac{( 3 b c a + b ^{2} c + b c ^{2} + c ^{2} a + c a ^{2} + b a ^{2} + b ^{2} a ) ^{2}}{b ^{2} c ^{2} + 2 b c ^{2} a + 2 b ^{2} c a + 2 b c a ^{2} + b ^{2} a ^{2} + c ^{2} a ^{2}}

x - 1 = \frac{( 3 b c a + b ^{2} c + b c ^{2} + c ^{2} a + c a ^{2} + b a ^{2} + b ^{2} a ) ^{2}}{b ^{2} c ^{2} + 2 b c ^{2} a + 2 b ^{2} c a + 2 b c a ^{2} + b ^{2} a ^{2} + c ^{2} a ^{2}}

解く

x - 1 = \frac{( 3 b c a + b ^{2} c + b c ^{2} + c ^{2} a + c a ^{2} + b a ^{2} + b ^{2} a ) ^{2}}{b ^{2} c ^{2} + 2 b c ^{2} a + 2 b ^{2} c a + 2 b c a ^{2} + b ^{2} a ^{2} + c ^{2} a ^{2}} : x = \frac{( 3 b c a + b ^{2} c + b c ^{2} + c ^{2} a + c a ^{2} + b a ^{2} + b ^{2} a ) ^{2}}{b ^{2} c ^{2} + 2 b c ^{2} a + 2 b ^{2} c a + 2 b c a ^{2} + b ^{2} a ^{2} + c ^{2} a ^{2}} + 1

x = \frac{( 3 b c a + b ^{2} c + b c ^{2} + c ^{2} a + c a ^{2} + b a ^{2} + b ^{2} a ) ^{2}}{b ^{2} c ^{2} + 2 b c ^{2} a + 2 b ^{2} c a + 2 b c a ^{2} + b ^{2} a ^{2} + c ^{2} a ^{2}} + 1

グラフ

人気の例

2sqrt(5-4x)=-12

2 5 - 4 x = - 12

sqrt(4x-3)+sqrt(2x+3)=6

4 x - 3 + 2 x + 3 = 6

3sqrt(2x)+4sqrt(2x)=10+2sqrt(2x)

3 2 x + 4 2 x = 10 + 2 2 x

sqrt(4x-8)-1=sqrt(2x-5)

4 x - 8 - 1 = 2 x - 5

sqrt(x+7)+sqrt(x-1)-2sqrt(x+2)=0

x + 7 + x - 1 - 2 x + 2 = 0