Issolvi {l}{(sqrt{2}-1)^2+(2sqrt{2}-1)^2}{+2sqrt{2}}

$$\left. \begin{array} { l } { ( \sqrt { 2 } - 1 ) ^ { 2 } + ( 2 \sqrt { 2 } - 1 ) ^ { 2 } } \\ { + 2 \sqrt { 2 } } \end{array} \right.$$

Evalwa

$$12-4\sqrt{2}\approx 6.343145751$$

Passi tas-Soluzzjonijiet

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

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

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

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

Żid 2 u 1 biex tikseb 3.

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

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

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

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

$$3-2\sqrt{2}+4\times 2-4\sqrt{2}+1+2\sqrt{2}$$

Immultiplika 4 u 2 biex tikseb 8.

$$3-2\sqrt{2}+8-4\sqrt{2}+1+2\sqrt{2}$$

Żid 8 u 1 biex tikseb 9.

$$3-2\sqrt{2}+9-4\sqrt{2}+2\sqrt{2}$$

Żid 3 u 9 biex tikseb 12.

$$12-2\sqrt{2}-4\sqrt{2}+2\sqrt{2}$$

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

$$12-6\sqrt{2}+2\sqrt{2}$$

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

$$12-4\sqrt{2}$$