Issolvi (2sqrt{3}-1)^2+(2sqrt{3}+1)^2=

$$( 2 \sqrt { 3 } - 1 ) ^ { 2 } + ( 2 \sqrt { 3 } + 1 ) ^ { 2 } =$$

Evalwa

$$26$$

Passi tas-Soluzzjonijiet

Uża teorema binomjali \left(a-b\right)^{2}=a^{2}-2ab+b^{2} biex tespandi \left(2\sqrt{3}-1\right)^{2}.

$$4\left(\sqrt{3}\right)^{2}-4\sqrt{3}+1+\left(2\sqrt{3}+1\right)^{2}$$

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

$$4\times 3-4\sqrt{3}+1+\left(2\sqrt{3}+1\right)^{2}$$

Immultiplika 4 u 3 biex tikseb 12.

$$12-4\sqrt{3}+1+\left(2\sqrt{3}+1\right)^{2}$$

Żid 12 u 1 biex tikseb 13.

$$13-4\sqrt{3}+\left(2\sqrt{3}+1\right)^{2}$$

Uża teorema binomjali \left(a+b\right)^{2}=a^{2}+2ab+b^{2} biex tespandi \left(2\sqrt{3}+1\right)^{2}.

$$13-4\sqrt{3}+4\left(\sqrt{3}\right)^{2}+4\sqrt{3}+1$$

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

$$13-4\sqrt{3}+4\times 3+4\sqrt{3}+1$$

Immultiplika 4 u 3 biex tikseb 12.

$$13-4\sqrt{3}+12+4\sqrt{3}+1$$

Żid 12 u 1 biex tikseb 13.

$$13-4\sqrt{3}+13+4\sqrt{3}$$

Żid 13 u 13 biex tikseb 26.

$$26-4\sqrt{3}+4\sqrt{3}$$

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

$$26$$

Fattur

$$2\times 13$$