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

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

Enrhifo

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

Camau Ateb

Defnyddio'r theorem binomaidd \left(a-b\right)^{2}=a^{2}-2ab+b^{2} i ehangu'r \left(5\sqrt{2}-4\right)^{2}.

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

Sgwâr \sqrt{2} yw 2.

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

Lluosi 25 a 2 i gael 50.

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

Adio 50 a 16 i gael 66.

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

Defnyddio'r theorem binomaidd \left(a-b\right)^{2}=a^{2}-2ab+b^{2} i ehangu'r \left(3-\sqrt{2}\right)^{2}.

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

Sgwâr \sqrt{2} yw 2.

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

Adio 9 a 2 i gael 11.

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

I ddod o hyd i wrthwyneb 11-6\sqrt{2}, dewch o hyd i wrthwyneb pob term.

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

Tynnu 11 o 66 i gael 55.

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

Cyfuno -40\sqrt{2} a 6\sqrt{2} i gael -34\sqrt{2}.

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

Ehangu

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

Camau Ateb

Defnyddio'r theorem binomaidd \left(a-b\right)^{2}=a^{2}-2ab+b^{2} i ehangu'r \left(5\sqrt{2}-4\right)^{2}.

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

Sgwâr \sqrt{2} yw 2.

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

Lluosi 25 a 2 i gael 50.

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

Adio 50 a 16 i gael 66.

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

Defnyddio'r theorem binomaidd \left(a-b\right)^{2}=a^{2}-2ab+b^{2} i ehangu'r \left(3-\sqrt{2}\right)^{2}.

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

Sgwâr \sqrt{2} yw 2.

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

Adio 9 a 2 i gael 11.

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

I ddod o hyd i wrthwyneb 11-6\sqrt{2}, dewch o hyd i wrthwyneb pob term.

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

Tynnu 11 o 66 i gael 55.

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

Cyfuno -40\sqrt{2} a 6\sqrt{2} i gael -34\sqrt{2}.

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