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

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

Evalwa

$$10\sqrt{2}+3\approx 17.142135624$$

Passi tas-Soluzzjonijiet

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

$$9+6\sqrt{2}+\left(\sqrt{2}\right)^{2}-4\left(2-\sqrt{2}\right)$$

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

$$9+6\sqrt{2}+2-4\left(2-\sqrt{2}\right)$$

Żid 9 u 2 biex tikseb 11.

$$11+6\sqrt{2}-4\left(2-\sqrt{2}\right)$$

Uża l-propjetà distributtiva biex timmultiplika -4 b'2-\sqrt{2}.

$$11+6\sqrt{2}-8+4\sqrt{2}$$

Naqqas 8 minn 11 biex tikseb 3.

$$3+6\sqrt{2}+4\sqrt{2}$$

Ikkombina 6\sqrt{2} u 4\sqrt{2} biex tikseb 10\sqrt{2}.

$$3+10\sqrt{2}$$