Issolvi 3*(2+sqrt{7})^2-12*(2+sqrt{7})+13

$$3 \times ( 2 + \sqrt { 7 } ) ^ { 2 } - 12 \times ( 2 + \sqrt { 7 } ) + 13$$

Evalwa

$$22$$

Passi tas-Soluzzjonijiet

Uża teorema binomjali \left(a+b\right)^{2}=a^{2}+2ab+b^{2} biex tespandi \left(2+\sqrt{7}\right)^{2}.

$$3\left(4+4\sqrt{7}+\left(\sqrt{7}\right)^{2}\right)-12\left(2+\sqrt{7}\right)+13$$

Il-kwadrat ta' \sqrt{7} huwa 7.

$$3\left(4+4\sqrt{7}+7\right)-12\left(2+\sqrt{7}\right)+13$$

Żid 4 u 7 biex tikseb 11.

$$3\left(11+4\sqrt{7}\right)-12\left(2+\sqrt{7}\right)+13$$

Uża l-propjetà distributtiva biex timmultiplika 3 b'11+4\sqrt{7}.

$$33+12\sqrt{7}-12\left(2+\sqrt{7}\right)+13$$

Uża l-propjetà distributtiva biex timmultiplika -12 b'2+\sqrt{7}.

$$33+12\sqrt{7}-24-12\sqrt{7}+13$$

Naqqas 24 minn 33 biex tikseb 9.

$$9+12\sqrt{7}-12\sqrt{7}+13$$

Ikkombina 12\sqrt{7} u -12\sqrt{7} biex tikseb 0.

$$9+13$$

Żid 9 u 13 biex tikseb 22.

$$22$$

Fattur

$$2\times 11$$