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

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

Arvuta

$$55-34\sqrt{2}\approx 6,916738879$$

Lahenduse etapid

Kasutage kaksliikme \left(5\sqrt{2}-4\right)^{2} arendamiseks binoomvalemit \left(a-b\right)^{2}=a^{2}-2ab+b^{2}.

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

\sqrt{2} ruut on 2.

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

Korrutage 25 ja 2, et leida 50.

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

Liitke 50 ja 16, et leida 66.

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

Kasutage kaksliikme \left(3-\sqrt{2}\right)^{2} arendamiseks binoomvalemit \left(a-b\right)^{2}=a^{2}-2ab+b^{2}.

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

\sqrt{2} ruut on 2.

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

Liitke 9 ja 2, et leida 11.

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

Avaldise "11-6\sqrt{2}" vastandi leidmiseks tuleb leida iga liikme vastand.

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

Lahutage 11 väärtusest 66, et leida 55.

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

Kombineerige -40\sqrt{2} ja 6\sqrt{2}, et leida -34\sqrt{2}.

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

Laienda

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

Lahenduse etapid

Kasutage kaksliikme \left(5\sqrt{2}-4\right)^{2} arendamiseks binoomvalemit \left(a-b\right)^{2}=a^{2}-2ab+b^{2}.

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

\sqrt{2} ruut on 2.

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

Korrutage 25 ja 2, et leida 50.

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

Liitke 50 ja 16, et leida 66.

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

Kasutage kaksliikme \left(3-\sqrt{2}\right)^{2} arendamiseks binoomvalemit \left(a-b\right)^{2}=a^{2}-2ab+b^{2}.

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

\sqrt{2} ruut on 2.

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

Liitke 9 ja 2, et leida 11.

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

Avaldise "11-6\sqrt{2}" vastandi leidmiseks tuleb leida iga liikme vastand.

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

Lahutage 11 väärtusest 66, et leida 55.

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

Kombineerige -40\sqrt{2} ja 6\sqrt{2}, et leida -34\sqrt{2}.

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