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Beliebt Algebra >

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

Lösung

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

Lösung

x = \frac{b ^{2}}{2 a ^{2}} + \frac{b b ^{2} - 4 ab}{2 a ^{2}} - \frac{b}{a}, x = \frac{b ^{2}}{2 a ^{2}} - \frac{b}{a} - \frac{b b ^{2} - 4 ab}{2 a ^{2}}

Schritte zur Lösung

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

Schreibe die Gleichung um mit

x = u

u^{2} \frac{a ( 1 + u )}{u ^{2} - 1} = b

Löse

u^{2} \frac{a ( 1 + u )}{u ^{2} - 1} = b : u = \frac{b + b ^{2} - 4 ab}{2 a}, u = \frac{b - b ^{2} - 4 ab}{2 a}

u = \frac{b + b ^{2} - 4 ab}{2 a}, u = \frac{b - b ^{2} - 4 ab}{2 a}

Setze

u = x w i e d er e in,

löse für

x

Löse

x = \frac{b + b ^{2} - 4 ab}{2 a} : x = \frac{b ^{2}}{2 a ^{2}} + \frac{b b ^{2} - 4 ab}{2 a ^{2}} - \frac{b}{a}

Löse

x = \frac{b - b ^{2} - 4 ab}{2 a} : x = \frac{b ^{2}}{2 a ^{2}} - \frac{b}{a} - \frac{b b ^{2} - 4 ab}{2 a ^{2}}

x = \frac{b ^{2}}{2 a ^{2}} + \frac{b b ^{2} - 4 ab}{2 a ^{2}} - \frac{b}{a}, x = \frac{b ^{2}}{2 a ^{2}} - \frac{b}{a} - \frac{b b ^{2} - 4 ab}{2 a ^{2}}

Graph

Beliebte Beispiele

(x - 5)^{\frac{4}{3}} = 16

2 = 9 + 9 x + 1

solvefor a,sqrt(a+b)=c

so l v e f or a, a + b = c

8 x - 4 = 5 x^{0.9}

x = a x + b