Issolvi (2+sqrt{3})^2+(2-sqrt{3})^2+16

$$( 2 + \sqrt { 3 } ) ^ { 2 } + ( 2 - \sqrt { 3 } ) ^ { 2 } + 16$$

Evalwa

$$30$$

Passi tas-Soluzzjonijiet

Uża teorema binomjali \left(a+b\right)^{2}=a^{2}+2ab+b^{2} biex tespandi \left(2+\sqrt{3}\right)^{2}.

$$4+4\sqrt{3}+\left(\sqrt{3}\right)^{2}+\left(2-\sqrt{3}\right)^{2}+16$$

Il-kwadrat ta' \sqrt{3} huwa 3.

$$4+4\sqrt{3}+3+\left(2-\sqrt{3}\right)^{2}+16$$

Żid 4 u 3 biex tikseb 7.

$$7+4\sqrt{3}+\left(2-\sqrt{3}\right)^{2}+16$$

Uża teorema binomjali \left(a-b\right)^{2}=a^{2}-2ab+b^{2} biex tespandi \left(2-\sqrt{3}\right)^{2}.

$$7+4\sqrt{3}+4-4\sqrt{3}+\left(\sqrt{3}\right)^{2}+16$$

Il-kwadrat ta' \sqrt{3} huwa 3.

$$7+4\sqrt{3}+4-4\sqrt{3}+3+16$$

Żid 4 u 3 biex tikseb 7.

$$7+4\sqrt{3}+7-4\sqrt{3}+16$$

Żid 7 u 7 biex tikseb 14.

$$14+4\sqrt{3}-4\sqrt{3}+16$$

Ikkombina 4\sqrt{3} u -4\sqrt{3} biex tikseb 0.

$$14+16$$

Żid 14 u 16 biex tikseb 30.

$$30$$

Fattur

$$2\times 3\times 5$$