b=(ax)/(1+asqrt(1-x^2))

Lösung

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

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

Schritte zur Lösung

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

Multipliziere beide Seiten mit

1 + a 1 - x^{2}

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

Vereinfache

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

Schreibe

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

um:

b + ba 1 - x^{2}

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

Quadratwurzeln entfernen

b^{2} a^{2} - b^{2} a^{2} x^{2} = a^{2} x^{2} - 2 ba x + b^{2}

Löse

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

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

2 (x + 1)^{\frac{2}{3}} = 18

so l v e f or x, y + x = 1

so l v e f or x, f = x

x - 7 + x = 1

3 4 x - 5 + 7 = 8