(3+sqrt{2})^2-4(2-sqrt{2}) eching

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

Baholash

$$10\sqrt{2}+3\approx 17,142135624$$

Yechim qadamlari

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

$$9+6\sqrt{2}+\left(\sqrt{2}\right)^{2}-4\left(2-\sqrt{2}\right)$$

\sqrt{2} kvadrati – 2.

$$9+6\sqrt{2}+2-4\left(2-\sqrt{2}\right)$$

11 olish uchun 9 va 2'ni qo'shing.

$$11+6\sqrt{2}-4\left(2-\sqrt{2}\right)$$

-4 ga 2-\sqrt{2} ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$11+6\sqrt{2}-8+4\sqrt{2}$$

3 olish uchun 11 dan 8 ni ayirish.

$$3+6\sqrt{2}+4\sqrt{2}$$

10\sqrt{2} ni olish uchun 6\sqrt{2} va 4\sqrt{2} ni birlashtirish.

$$3+10\sqrt{2}$$