Issolvi (5sqrt{2}-4)^2-(3-sqrt{2})^2

$$( 5 \sqrt { 2 } - 4 ) ^ { 2 } - ( 3 - \sqrt { 2 } ) ^ { 2 }$$

Evalwa

$$55-34\sqrt{2}\approx 6.916738879$$

Passi tas-Soluzzjonijiet

Uża teorema binomjali \left(a-b\right)^{2}=a^{2}-2ab+b^{2} biex tespandi \left(5\sqrt{2}-4\right)^{2}.

$$25\left(\sqrt{2}\right)^{2}-40\sqrt{2}+16-\left(3-\sqrt{2}\right)^{2}$$

Il-kwadrat ta' \sqrt{2} huwa 2.

$$25\times 2-40\sqrt{2}+16-\left(3-\sqrt{2}\right)^{2}$$

Immultiplika 25 u 2 biex tikseb 50.

$$50-40\sqrt{2}+16-\left(3-\sqrt{2}\right)^{2}$$

Żid 50 u 16 biex tikseb 66.

$$66-40\sqrt{2}-\left(3-\sqrt{2}\right)^{2}$$

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

$$66-40\sqrt{2}-\left(9-6\sqrt{2}+\left(\sqrt{2}\right)^{2}\right)$$

Il-kwadrat ta' \sqrt{2} huwa 2.

$$66-40\sqrt{2}-\left(9-6\sqrt{2}+2\right)$$

Żid 9 u 2 biex tikseb 11.

$$66-40\sqrt{2}-\left(11-6\sqrt{2}\right)$$

Biex issib l-oppost ta' 11-6\sqrt{2}, sib l-oppost ta' kull terminu.

$$66-40\sqrt{2}-11+6\sqrt{2}$$

Naqqas 11 minn 66 biex tikseb 55.

$$55-40\sqrt{2}+6\sqrt{2}$$

Ikkombina -40\sqrt{2} u 6\sqrt{2} biex tikseb -34\sqrt{2}.

$$55-34\sqrt{2}$$

Espandi

$$55-34\sqrt{2}$$

Passi tas-Soluzzjonijiet

Uża teorema binomjali \left(a-b\right)^{2}=a^{2}-2ab+b^{2} biex tespandi \left(5\sqrt{2}-4\right)^{2}.

$$25\left(\sqrt{2}\right)^{2}-40\sqrt{2}+16-\left(3-\sqrt{2}\right)^{2}$$

Il-kwadrat ta' \sqrt{2} huwa 2.

$$25\times 2-40\sqrt{2}+16-\left(3-\sqrt{2}\right)^{2}$$

Immultiplika 25 u 2 biex tikseb 50.

$$50-40\sqrt{2}+16-\left(3-\sqrt{2}\right)^{2}$$

Żid 50 u 16 biex tikseb 66.

$$66-40\sqrt{2}-\left(3-\sqrt{2}\right)^{2}$$

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

$$66-40\sqrt{2}-\left(9-6\sqrt{2}+\left(\sqrt{2}\right)^{2}\right)$$

Il-kwadrat ta' \sqrt{2} huwa 2.

$$66-40\sqrt{2}-\left(9-6\sqrt{2}+2\right)$$

Żid 9 u 2 biex tikseb 11.

$$66-40\sqrt{2}-\left(11-6\sqrt{2}\right)$$

Biex issib l-oppost ta' 11-6\sqrt{2}, sib l-oppost ta' kull terminu.

$$66-40\sqrt{2}-11+6\sqrt{2}$$

Naqqas 11 minn 66 biex tikseb 55.

$$55-40\sqrt{2}+6\sqrt{2}$$

Ikkombina -40\sqrt{2} u 6\sqrt{2} biex tikseb -34\sqrt{2}.

$$55-34\sqrt{2}$$