Resolver S=-3/2(m-3/2)^2

$$S = - \frac { 3 } { 2 } ( m - \frac { 3 } { 2 } ) ^ { 2 }$$

Ebatzi: S

$$S=-\frac{3\left(2m-3\right)^{2}}{8}$$

Ebazpidea

\left(m-\frac{3}{2}\right)^{2} zabaltzeko, erabili Newton-en binomioa \left(a-b\right)^{2}=a^{2}-2ab+b^{2}.

$$S=-\frac{3}{2}\left(m^{2}-3m+\frac{9}{4}\right)$$

Erabili banaketa-propietatea -\frac{3}{2} eta m^{2}-3m+\frac{9}{4} biderkatzeko.

$$S=-\frac{3}{2}m^{2}+\frac{9}{2}m-\frac{27}{8}$$

Ebatzi: m (complex solution)

$$m=-\frac{i\sqrt{6S}}{3}+\frac{3}{2}$$

$$m=\frac{i\sqrt{6S}}{3}+\frac{3}{2}$$

Ebatzi: m

$$m=-\frac{\sqrt{-6S}}{3}+\frac{3}{2}$$

$$m=\frac{\sqrt{-6S}}{3}+\frac{3}{2}\text{, }S\leq 0$$