Issolvi M=(-b+1/2a)^2-(b-b(a-3))-(ab^3-0.75a^3b):(ab)

$$M = ( - b + \frac { 1 } { 2 } a ) ^ { 2 } - ( b - b ( a - 3 ) ) - ( a b ^ { 3 } - 0.75 a ^ { 3 } b ) : ( a b )$$

Solvi għal M

$$M=a^{2}-4b$$

$$a\neq 0\text{ and }b\neq 0$$

Passi Qosra tas-Soluzzjonijiet

Uża teorema binomjali \left(p+q\right)^{2}=p^{2}+2pq+q^{2} biex tespandi \left(-b+\frac{1}{2}a\right)^{2}.

$$M=\left(-b\right)^{2}+\left(-b\right)a+\frac{1}{4}a^{2}-\left(b-b\left(a-3\right)\right)-\frac{ab^{3}-0.75a^{3}b}{ab}$$

Ikkalkula -b bil-power ta' 2 u tikseb b^{2}.

$$M=b^{2}+\left(-b\right)a+\frac{1}{4}a^{2}-\left(b-b\left(a-3\right)\right)-\frac{ab^{3}-0.75a^{3}b}{ab}$$

Uża l-propjetà distributtiva biex timmultiplika b b'a-3.

$$M=b^{2}+\left(-b\right)a+\frac{1}{4}a^{2}-\left(b-\left(ba-3b\right)\right)-\frac{ab^{3}-0.75a^{3}b}{ab}$$

Biex issib l-oppost ta' ba-3b, sib l-oppost ta' kull terminu.

$$M=b^{2}+\left(-b\right)a+\frac{1}{4}a^{2}-\left(b-ba+3b\right)-\frac{ab^{3}-0.75a^{3}b}{ab}$$

Ikkombina b u 3b biex tikseb 4b.

$$M=b^{2}+\left(-b\right)a+\frac{1}{4}a^{2}-\left(4b-ba\right)-\frac{ab^{3}-0.75a^{3}b}{ab}$$

Biex issib l-oppost ta' 4b-ba, sib l-oppost ta' kull terminu.

$$M=b^{2}+\left(-b\right)a+\frac{1}{4}a^{2}-4b+ba-\frac{ab^{3}-0.75a^{3}b}{ab}$$

Iffattura l-espressjonijiet li mhumiex diġà fatturati f'\frac{ab^{3}-0.75a^{3}b}{ab}.

$$M=b^{2}+\left(-b\right)a+\frac{1}{4}a^{2}-4b+ba-\frac{0.25ab\left(-3a^{2}+4b^{2}\right)}{ab}$$

Annulla ab fin-numeratur u d-denominatur.

$$M=b^{2}+\left(-b\right)a+\frac{1}{4}a^{2}-4b+ba-0.25\left(-3a^{2}+4b^{2}\right)$$

Espandi l-espressjoni.

$$M=b^{2}+\left(-b\right)a+\frac{1}{4}a^{2}-4b+ba-\left(-0.75a^{2}+b^{2}\right)$$

Biex issib l-oppost ta' -0.75a^{2}+b^{2}, sib l-oppost ta' kull terminu.

$$M=b^{2}+\left(-b\right)a+\frac{1}{4}a^{2}-4b+ba+0.75a^{2}-b^{2}$$

Ikkombina \frac{1}{4}a^{2} u 0.75a^{2} biex tikseb a^{2}.

$$M=b^{2}+\left(-b\right)a+a^{2}-4b+ba-b^{2}$$

Ikkombina b^{2} u -b^{2} biex tikseb 0.

$$M=\left(-b\right)a+a^{2}-4b+ba$$

Ikkombina -ba u ba biex tikseb 0.

$$M=a^{2}-4b$$

Solvi għal a (complex solution)

$$a=-\sqrt{M+4b}$$

$$a=\sqrt{M+4b}\text{, }M\neq -4b\text{ and }b\neq 0$$

Solvi għal a

$$a=\sqrt{M+4b}$$

$$a=-\sqrt{M+4b}\text{, }M>-4b\text{ and }b\neq 0$$