vereinfachen (sqrt(x^2+x-2)+sqrt((3-x)(x+2)))^2

Lösung

vereinfachen

(x^{2} + x - 2 + (3 - x) (x + 2))^{2}

2 x + 2 (3 - x) (x + 2) x^{2} + x - 2 + 4

Schritte zur Lösung

(x^{2} + x - 2 + (3 - x) (x + 2))^{2}

Wende Formel für perfekte quadratische Gleichungen an:

(a + b)^{2} = a^{2} + 2 ab + b^{2}

(x^{2} + x - 2 + (3 - x) (x + 2))^{2} = (x^{2} + x - 2)^{2} + 2 x^{2} + x - 2 (3 - x) (x + 2) + ((3 - x) (x + 2))^{2}

= (x^{2} + x - 2)^{2} + 2 x^{2} + x - 2 (3 - x) (x + 2) + ((3 - x) (x + 2))^{2}

Vereinfache

(x^{2} + x - 2)^{2} + 2 x^{2} + x - 2 (3 - x) (x + 2) + ((3 - x) (x + 2))^{2} : 2 x + 2 (3 - x) (x + 2) x^{2} + x - 2 + 4

= 2 x + 2 (3 - x) (x + 2) x^{2} + x - 2 + 4

s im pl i f y t (x) x^{^{''}} + (2 t (x) - 4) x^{^{'}} + 2 x

e x p an d s + i (- s^{2} + 1)

e x p an d \frac{s ^{2} + 20 s + 150}{( s + 2.93 ) ( s + 17.07 )}

e x p an d \frac{4 ( s + 1 )}{( s ^{2} + 2 s + 5 ) ^{2}}

e x p an d (4, 7) y (3, - 2)