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

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

Whakaoti mō M

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

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

Ngā Hipanga Rongoā Poto

Whakamahia te ture huarua \left(p+q\right)^{2}=p^{2}+2pq+q^{2} hei whakaroha \left(-b+\frac{1}{2}a\right)^{2}.

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

Tātaihia te -b mā te pū o 2, kia riro ko b^{2}.

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

Whakamahia te āhuatanga tohatoha hei whakarea te b ki te a-3.

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

Hei kimi i te tauaro o ba-3b, kimihia te tauaro o ia taurangi.

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

Pahekotia te b me 3b, ka 4b.

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

Hei kimi i te tauaro o 4b-ba, kimihia te tauaro o ia taurangi.

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

Me whakatauwehe ngā kīanga kāore anō i whakatauwehea i roto o \frac{ab^{3}-0.75a^{3}b}{ab}.

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

Me whakakore tahi te ab i te taurunga me te tauraro.

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

Me whakaroha te kīanga.

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

Hei kimi i te tauaro o -0.75a^{2}+b^{2}, kimihia te tauaro o ia taurangi.

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

Pahekotia te \frac{1}{4}a^{2} me 0.75a^{2}, ka a^{2}.

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

Pahekotia te b^{2} me -b^{2}, ka 0.

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

Pahekotia te -ba me ba, ka 0.

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

Whakaoti mō a (complex solution)

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

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

Whakaoti mō a

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

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