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

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

Réitigh do M.

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

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

Céimeanna gearra réitigh

Úsáid an teoirim dhéthéarmach \left(p+q\right)^{2}=p^{2}+2pq+q^{2} chun \left(-b+\frac{1}{2}a\right)^{2} a leathnú.

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

Ríomh cumhacht -b de 2 agus faigh b^{2}.

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

Úsáid an t-airí dáileach chun b a mhéadú faoi a-3.

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

Chun an mhalairt ar ba-3b a aimsiú, aimsigh an mhalairt ar gach téarma.

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

Comhcheangail b agus 3b chun 4b a fháil.

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

Chun an mhalairt ar 4b-ba a aimsiú, aimsigh an mhalairt ar gach téarma.

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

Fachtóirigh na sloinn nach bhfuil fachtóirithe cheana in \frac{ab^{3}-0.75a^{3}b}{ab}.

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

Cealaigh ab mar uimhreoir agus ainmneoir.

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

Fairsingigh an slonn.

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

Chun an mhalairt ar -0.75a^{2}+b^{2} a aimsiú, aimsigh an mhalairt ar gach téarma.

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

Comhcheangail \frac{1}{4}a^{2} agus 0.75a^{2} chun a^{2} a fháil.

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

Comhcheangail b^{2} agus -b^{2} chun 0 a fháil.

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

Comhcheangail -ba agus ba chun 0 a fháil.

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

Réitigh do a.

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

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