(1-sqrt{18})(sqrt{2}+1/sqrt{2}) eching

$$( 1 - \sqrt { 18 } ) ( \sqrt { 2 } + \frac { 1 } { \sqrt { 2 } } )$$

Baholash

$$\frac{3\left(\sqrt{2}-6\right)}{2}\approx -6,878679656$$

Yechim qadamlari

Faktor: 18=3^{2}\times 2. \sqrt{3^{2}\times 2} koʻpaytmasining kvadrat ildizini \sqrt{3^{2}}\sqrt{2} kvadrat ildizlarining koʻpaytmasi sifatida qayta yozing. 3^{2} ning kvadrat ildizini chiqarish.

$$\left(1-3\sqrt{2}\right)\left(\sqrt{2}+\frac{1}{\sqrt{2}}\right)$$

\frac{1}{\sqrt{2}} maxrajini \sqrt{2} orqali surat va maxrajini koʻpaytirish orqali ratsionallashtiring.

$$\left(1-3\sqrt{2}\right)\left(\sqrt{2}+\frac{\sqrt{2}}{\left(\sqrt{2}\right)^{2}}\right)$$

\sqrt{2} kvadrati – 2.

$$\left(1-3\sqrt{2}\right)\left(\sqrt{2}+\frac{\sqrt{2}}{2}\right)$$

\frac{3}{2}\sqrt{2} ni olish uchun \sqrt{2} va \frac{\sqrt{2}}{2} ni birlashtirish.

$$\left(1-3\sqrt{2}\right)\times \frac{3}{2}\sqrt{2}$$

1-3\sqrt{2} ga \frac{3}{2} ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$\left(\frac{3}{2}-3\sqrt{2}\times \frac{3}{2}\right)\sqrt{2}$$

-3\times \frac{3}{2} ni yagona kasrga aylantiring.

$$\left(\frac{3}{2}+\frac{-3\times 3}{2}\sqrt{2}\right)\sqrt{2}$$

-9 hosil qilish uchun -3 va 3 ni ko'paytirish.

$$\left(\frac{3}{2}+\frac{-9}{2}\sqrt{2}\right)\sqrt{2}$$

\frac{-9}{2} kasri manfiy belgini olib tashlash bilan -\frac{9}{2} sifatida qayta yozilishi mumkin.

$$\left(\frac{3}{2}-\frac{9}{2}\sqrt{2}\right)\sqrt{2}$$

\frac{3}{2}-\frac{9}{2}\sqrt{2} ga \sqrt{2} ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$\frac{3}{2}\sqrt{2}-\frac{9}{2}\sqrt{2}\sqrt{2}$$

2 hosil qilish uchun \sqrt{2} va \sqrt{2} ni ko'paytirish.

$$\frac{3}{2}\sqrt{2}-\frac{9}{2}\times 2$$

2 va 2 ni qisqartiring.

$$\frac{3}{2}\sqrt{2}-9$$

Omil

$$\frac{3 {(\sqrt{2} - 6)}}{2} = -6,878679656440358$$