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Популярное Алгебра >

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

Решение

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

Решение

x = \frac{a ^{3} + 4 a ^{2} b + 4 a ^{2} c + 4 a b ^{2} + 4 a c ^{2} + 9 ab c + b ^{3} + c ^{3} + 4 b c ^{2} + 4 b ^{2} c}{a ^{2} + b ^{2} + 3 ab + c ^{2} + 3 a c + 3 b c}; (b + c) (a + c) (a + b) \neq = 0, a \neq = \frac{- 3 b - 3 c + 5 b ^{2} + 6 b c + 5 c ^{2}}{2}, a \neq = \frac{- 3 b - 3 c - 5 b ^{2} + 6 b c + 5 c ^{2}}{2}

Шаги решения

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

Умножить на НОК

(x - a) (a + c) (a + b) + (x - b) (b + c) (a + b) + (x - c) (b + c) (a + c) = 3 (b + c) (a + c) (a + b); (b + c) (a + c) (a + b) \neq = 0

Расширить

(b + c) (a + c) : ab + b c + a c + c^{2}

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

Расширить

(ab + b c + a c + c^{2}) (a + b) : a^{2} b + a b^{2} + a c^{2} + 2 ab c + a^{2} c + b c^{2} + b^{2} c

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

Расширить

3 (a^{2} b + a b^{2} + a c^{2} + 2 ab c + a^{2} c + b c^{2} + b^{2} c) : 3 a^{2} b + 3 a b^{2} + 3 a c^{2} + 6 ab c + 3 a^{2} c + 3 b c^{2} + 3 b^{2} c

a^{2} x + b^{2} x + 3 ab x + c^{2} x + 3 a c x + 3 b c x - a^{3} - b^{3} - a b^{2} - a^{2} b - c^{3} - b c^{2} - a c^{2} - a^{2} c - 3 ab c - b^{2} c = 3 a^{2} b + 3 a b^{2} + 3 a c^{2} + 6 ab c + 3 a^{2} c + 3 b c^{2} + 3 b^{2} c

Расширьте

(x - a) (a + c) (a + b) + (x - b) (b + c) (a + b) + (x - c) (b + c) (a + c) : a^{2} x + b^{2} x + 3 ab x + c^{2} x + 3 a c x + 3 b c x - a^{3} - b^{3} - a b^{2} - a^{2} b - c^{3} - b c^{2} - a c^{2} - a^{2} c - 3 ab c - b^{2} c

a^{2} x + b^{2} x + 3 ab x + c^{2} x + 3 a c x + 3 b c x - a^{3} - b^{3} - a b^{2} - a^{2} b - c^{3} - b c^{2} - a c^{2} - a^{2} c - 3 ab c - b^{2} c = 3 a^{2} b + 3 a b^{2} + 3 a c^{2} + 6 ab c + 3 a^{2} c + 3 b c^{2} + 3 b^{2} c; (b + c) (a + c) (a + b) \neq = 0

Переместите

a^{3}

вправо

a^{2} x + b^{2} x + 3 ab x + c^{2} x + 3 a c x + 3 b c x - b^{3} - a b^{2} - a^{2} b - c^{3} - b c^{2} - a c^{2} - a^{2} c - 3 ab c - b^{2} c = 3 a^{2} b + 3 a b^{2} + 3 a c^{2} + 6 ab c + 3 a^{2} c + 3 b c^{2} + 3 b^{2} c + a^{3}; (b + c) (a + c) (a + b) \neq = 0

Переместите

b^{3}

вправо

a^{2} x + b^{2} x + 3 ab x + c^{2} x + 3 a c x + 3 b c x - a b^{2} - a^{2} b - c^{3} - b c^{2} - a c^{2} - a^{2} c - 3 ab c - b^{2} c = 3 a^{2} b + 3 a b^{2} + 3 a c^{2} + 6 ab c + 3 a^{2} c + 3 b c^{2} + 3 b^{2} c + a^{3} + b^{3}; (b + c) (a + c) (a + b) \neq = 0

Переместите

a b^{2}

вправо

a^{2} x + b^{2} x + 3 ab x + c^{2} x + 3 a c x + 3 b c x - a^{2} b - c^{3} - b c^{2} - a c^{2} - a^{2} c - 3 ab c - b^{2} c = a^{3} + 3 a^{2} b + 3 a^{2} c + 4 a b^{2} + 3 a c^{2} + 6 ab c + b^{3} + 3 b c^{2} + 3 b^{2} c; (b + c) (a + c) (a + b) \neq = 0

Переместите

a^{2} b

вправо

a^{2} x + b^{2} x + 3 ab x + c^{2} x + 3 a c x + 3 b c x - c^{3} - b c^{2} - a c^{2} - a^{2} c - 3 ab c - b^{2} c = a^{3} + 4 a^{2} b + 3 a^{2} c + 4 a b^{2} + 3 a c^{2} + 6 ab c + b^{3} + 3 b c^{2} + 3 b^{2} c; (b + c) (a + c) (a + b) \neq = 0

Переместите

c^{3}

вправо

a^{2} x + b^{2} x + 3 ab x + c^{2} x + 3 a c x + 3 b c x - b c^{2} - a c^{2} - a^{2} c - 3 ab c - b^{2} c = a^{3} + 4 a^{2} b + 3 a^{2} c + 4 a b^{2} + 3 a c^{2} + 6 ab c + b^{3} + 3 b c^{2} + 3 b^{2} c + c^{3}; (b + c) (a + c) (a + b) \neq = 0

Переместите

b c^{2}

вправо

a^{2} x + b^{2} x + 3 ab x + c^{2} x + 3 a c x + 3 b c x - a c^{2} - a^{2} c - 3 ab c - b^{2} c = b^{3} + 4 a b^{2} + 3 b^{2} c + 4 a^{2} b + 4 b c^{2} + 6 ab c + a^{3} + c^{3} + 3 a c^{2} + 3 a^{2} c; (b + c) (a + c) (a + b) \neq = 0

Переместите

a c^{2}

вправо

a^{2} x + b^{2} x + 3 ab x + c^{2} x + 3 a c x + 3 b c x - a^{2} c - 3 ab c - b^{2} c = a^{3} + 4 a^{2} b + 3 a^{2} c + 4 a b^{2} + 4 a c^{2} + 6 ab c + b^{3} + c^{3} + 4 b c^{2} + 3 b^{2} c; (b + c) (a + c) (a + b) \neq = 0

Переместите

a^{2} c

вправо

a^{2} x + b^{2} x + 3 ab x + c^{2} x + 3 a c x + 3 b c x - 3 ab c - b^{2} c = a^{3} + 4 a^{2} b + 4 a^{2} c + 4 a b^{2} + 4 a c^{2} + 6 ab c + b^{3} + c^{3} + 4 b c^{2} + 3 b^{2} c; (b + c) (a + c) (a + b) \neq = 0

Переместите

3 ab c

вправо

a^{2} x + b^{2} x + 3 ab x + c^{2} x + 3 a c x + 3 b c x - b^{2} c = a^{3} + 4 a^{2} b + 4 a^{2} c + 4 a b^{2} + 4 a c^{2} + 9 ab c + b^{3} + c^{3} + 4 b c^{2} + 3 b^{2} c; (b + c) (a + c) (a + b) \neq = 0

Переместите

b^{2} c

вправо

a^{2} x + b^{2} x + 3 ab x + c^{2} x + 3 a c x + 3 b c x = a^{3} + 4 a^{2} b + 4 a^{2} c + 4 a b^{2} + 4 a c^{2} + 9 ab c + b^{3} + c^{3} + 4 b c^{2} + 4 b^{2} c; (b + c) (a + c) (a + b) \neq = 0

коэффициент

a^{2} x + b^{2} x + 3 ab x + c^{2} x + 3 a c x + 3 b c x : x (a^{2} + b^{2} + 3 ab + c^{2} + 3 a c + 3 b c)

x (a^{2} + b^{2} + 3 ab + c^{2} + 3 a c + 3 b c) = a^{3} + 4 a^{2} b + 4 a^{2} c + 4 a b^{2} + 4 a c^{2} + 9 ab c + b^{3} + c^{3} + 4 b c^{2} + 4 b^{2} c; (b + c) (a + c) (a + b) \neq = 0

Разделите обе стороны на

a^{2} + b^{2} + 3 ab + c^{2} + 3 a c + 3 b c; (b + c) (a + c) (a + b) \neq = 0, a \neq = \frac{- 3 b - 3 c + 5 b ^{2} + 6 b c + 5 c ^{2}}{2}, a \neq = \frac{- 3 b - 3 c - 5 b ^{2} + 6 b c + 5 c ^{2}}{2}

x = \frac{a ^{3} + 4 a ^{2} b + 4 a ^{2} c + 4 a b ^{2} + 4 a c ^{2} + 9 ab c + b ^{3} + c ^{3} + 4 b c ^{2} + 4 b ^{2} c}{a ^{2} + b ^{2} + 3 ab + c ^{2} + 3 a c + 3 b c}; (b + c) (a + c) (a + b) \neq = 0, a \neq = \frac{- 3 b - 3 c + 5 b ^{2} + 6 b c + 5 c ^{2}}{2}, a \neq = \frac{- 3 b - 3 c - 5 b ^{2} + 6 b c + 5 c ^{2}}{2}

График

Популярные примеры

11 = x - 6

solvefor p,r=q+p+s

so l v e f or p, r = q + p + s

(x/4)+3=((2x)/6)-(1/16)

(\frac{x}{4}) + 3 = (\frac{2 x}{6}) - (\frac{1}{16})

ka (- 3) = a

solvefor m,x= m/p-(b/p)^{1/2}

so l v e f or m, x = \frac{m}{p} - (\frac{b}{p})^{\frac{1}{2}}