{left(7+3sqrt{2}right)}^2-{left(5-2sqrt{5}right)}^2 eching

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

Baholash

$$20\sqrt{5}+42\sqrt{2}+22\approx 126,11832917$$

Yechim qadamlari

\left(a+b\right)^{2}=a^{2}+2ab+b^{2} binom teoremasini \left(7+3\sqrt{2}\right)^{2} kengaytirilishi uchun ishlating.

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

\sqrt{2} kvadrati – 2.

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

18 hosil qilish uchun 9 va 2 ni ko'paytirish.

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

67 olish uchun 49 va 18'ni qo'shing.

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

\left(a-b\right)^{2}=a^{2}-2ab+b^{2} binom teoremasini \left(5-2\sqrt{5}\right)^{2} kengaytirilishi uchun ishlating.

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

\sqrt{5} kvadrati – 5.

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

20 hosil qilish uchun 4 va 5 ni ko'paytirish.

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

45 olish uchun 25 va 20'ni qo'shing.

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

45-20\sqrt{5} teskarisini topish uchun har birining teskarisini toping.

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

22 olish uchun 67 dan 45 ni ayirish.

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

Kengaytirish

$$20 \sqrt{5} + 42 \sqrt{2} + 22 = 126,11832917$$

Yechim qadamlari

\left(a+b\right)^{2}=a^{2}+2ab+b^{2} binom teoremasini \left(7+3\sqrt{2}\right)^{2} kengaytirilishi uchun ishlating.

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

\sqrt{2} kvadrati – 2.

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

18 hosil qilish uchun 9 va 2 ni ko'paytirish.

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

67 olish uchun 49 va 18'ni qo'shing.

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

\left(a-b\right)^{2}=a^{2}-2ab+b^{2} binom teoremasini \left(5-2\sqrt{5}\right)^{2} kengaytirilishi uchun ishlating.

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

\sqrt{5} kvadrati – 5.

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

20 hosil qilish uchun 4 va 5 ni ko'paytirish.

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

45 olish uchun 25 va 20'ni qo'shing.

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

45-20\sqrt{5} teskarisini topish uchun har birining teskarisini toping.

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

22 olish uchun 67 dan 45 ni ayirish.

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