Réitigh F=(4t-1)(4t+1)-(3t+2)^2

$$F = ( 4 t - 1 ) ( 4 t + 1 ) - ( 3 t + 2 ) ^ { 2 }$$

Réitigh do F.

$$F=7t^{2}-12t-5$$

Céimeanna Réitigh

Mar shampla \left(4t-1\right)\left(4t+1\right). Is féidir iolrúchán a athrú ó bhonn go dtí difríocht na gcearnóg ag úsáid na rialach seo: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}. Cearnóg 1.

$$F=\left(4t\right)^{2}-1-\left(3t+2\right)^{2}$$

Fairsingigh \left(4t\right)^{2}

$$F=4^{2}t^{2}-1-\left(3t+2\right)^{2}$$

Ríomh cumhacht 4 de 2 agus faigh 16.

$$F=16t^{2}-1-\left(3t+2\right)^{2}$$

Úsáid an teoirim dhéthéarmach \left(a+b\right)^{2}=a^{2}+2ab+b^{2} chun \left(3t+2\right)^{2} a leathnú.

$$F=16t^{2}-1-\left(9t^{2}+12t+4\right)$$

Chun an mhalairt ar 9t^{2}+12t+4 a aimsiú, aimsigh an mhalairt ar gach téarma.

$$F=16t^{2}-1-9t^{2}-12t-4$$

Comhcheangail 16t^{2} agus -9t^{2} chun 7t^{2} a fháil.

$$F=7t^{2}-1-12t-4$$

Dealaigh 4 ó -1 chun -5 a fháil.

$$F=7t^{2}-5-12t$$

Réitigh do t.

$$t=\frac{-\sqrt{7F+71}+6}{7}$$

$$t=\frac{\sqrt{7F+71}+6}{7}\text{, }F\geq -\frac{71}{7}$$