Datrys (7+3sqrt{2})^2-(5-2sqrt{5})^2

$$( 7 + 3 \sqrt { 2 } ) ^ { 2 } - ( 5 - 2 \sqrt { 5 } ) ^ { 2 }$$

Enrhifo

$$20\sqrt{5}+42\sqrt{2}+22\approx 126.11832917$$

Camau Ateb

Defnyddio'r theorem binomaidd \left(a+b\right)^{2}=a^{2}+2ab+b^{2} i ehangu'r \left(7+3\sqrt{2}\right)^{2}.

$$49+42\sqrt{2}+9\left(\sqrt{2}\right)^{2}-\left(5-2\sqrt{5}\right)^{2}$$

Sgwâr \sqrt{2} yw 2.

$$49+42\sqrt{2}+9\times 2-\left(5-2\sqrt{5}\right)^{2}$$

Lluosi 9 a 2 i gael 18.

$$49+42\sqrt{2}+18-\left(5-2\sqrt{5}\right)^{2}$$

Adio 49 a 18 i gael 67.

$$67+42\sqrt{2}-\left(5-2\sqrt{5}\right)^{2}$$

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

$$67+42\sqrt{2}-\left(25-20\sqrt{5}+4\left(\sqrt{5}\right)^{2}\right)$$

Sgwâr \sqrt{5} yw 5.

$$67+42\sqrt{2}-\left(25-20\sqrt{5}+4\times 5\right)$$

Lluosi 4 a 5 i gael 20.

$$67+42\sqrt{2}-\left(25-20\sqrt{5}+20\right)$$

Adio 25 a 20 i gael 45.

$$67+42\sqrt{2}-\left(45-20\sqrt{5}\right)$$

I ddod o hyd i wrthwyneb 45-20\sqrt{5}, dewch o hyd i wrthwyneb pob term.

$$67+42\sqrt{2}-45+20\sqrt{5}$$

Tynnu 45 o 67 i gael 22.

$$22+42\sqrt{2}+20\sqrt{5}$$

Ehangu

$$20 \sqrt{5} + 42 \sqrt{2} + 22 = 126.11832917$$

Camau Ateb

Defnyddio'r theorem binomaidd \left(a+b\right)^{2}=a^{2}+2ab+b^{2} i ehangu'r \left(7+3\sqrt{2}\right)^{2}.

$$49+42\sqrt{2}+9\left(\sqrt{2}\right)^{2}-\left(5-2\sqrt{5}\right)^{2}$$

Sgwâr \sqrt{2} yw 2.

$$49+42\sqrt{2}+9\times 2-\left(5-2\sqrt{5}\right)^{2}$$

Lluosi 9 a 2 i gael 18.

$$49+42\sqrt{2}+18-\left(5-2\sqrt{5}\right)^{2}$$

Adio 49 a 18 i gael 67.

$$67+42\sqrt{2}-\left(5-2\sqrt{5}\right)^{2}$$

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

$$67+42\sqrt{2}-\left(25-20\sqrt{5}+4\left(\sqrt{5}\right)^{2}\right)$$

Sgwâr \sqrt{5} yw 5.

$$67+42\sqrt{2}-\left(25-20\sqrt{5}+4\times 5\right)$$

Lluosi 4 a 5 i gael 20.

$$67+42\sqrt{2}-\left(25-20\sqrt{5}+20\right)$$

Adio 25 a 20 i gael 45.

$$67+42\sqrt{2}-\left(45-20\sqrt{5}\right)$$

I ddod o hyd i wrthwyneb 45-20\sqrt{5}, dewch o hyd i wrthwyneb pob term.

$$67+42\sqrt{2}-45+20\sqrt{5}$$

Tynnu 45 o 67 i gael 22.

$$22+42\sqrt{2}+20\sqrt{5}$$