Whakaoti i te (2m-1)^2-4(m^2-1)>0

$$( 2 m - 1 ) ^ { 2 } - 4 ( m ^ { 2 } - 1 ) > 0$$

Whakaoti mō m

$$m<\frac{5}{4}$$

Ngā Upane Otinga

Whakamahia te ture huarua \left(a-b\right)^{2}=a^{2}-2ab+b^{2} hei whakaroha \left(2m-1\right)^{2}.

$$4m^{2}-4m+1-4\left(m^{2}-1\right)>0$$

Whakamahia te āhuatanga tohatoha hei whakarea te -4 ki te m^{2}-1.

$$4m^{2}-4m+1-4m^{2}+4>0$$

Pahekotia te 4m^{2} me -4m^{2}, ka 0.

$$-4m+1+4>0$$

Tāpirihia te 1 ki te 4, ka 5.

$$-4m+5>0$$

Tangohia te 5 mai i ngā taha e rua. Ko te tau i tango i te kore ka hua ko tōna korenga.

$$-4m>-5$$

Whakawehea ngā taha e rua ki te -4. I te mea he tōraro a -4, ka huri te ahunga koreōrite.

$$m<\frac{-5}{-4}$$

Ka taea te hautanga \frac{-5}{-4} te whakamāmā ki te \frac{5}{4} mā te tango tahi i te tohu tōraro i te taurunga me te tauraro.

$$m<\frac{5}{4}$$