(sqrt{-1}+sqrt{-2}-sqrt{-3})(sqrt{-1}-sqrt{-2}+sqrt{-3}) eching

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

Baholash (complex solution)

$$4-2\sqrt{6}\approx -0,898979486$$

Yechim qadamlari

-1 ning kvadrat ildizini hisoblab, i natijaga ega bo‘ling.

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

Faktor: -2=2\left(-1\right). \sqrt{2\left(-1\right)} koʻpaytmasining kvadrat ildizini \sqrt{2}\sqrt{-1} kvadrat ildizlarining koʻpaytmasi sifatida qayta yozing. Ta’rifi bo‘yicha, -1 ning kvadrat ildizi i ga teng.

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

Faktor: -3=3\left(-1\right). \sqrt{3\left(-1\right)} koʻpaytmasining kvadrat ildizini \sqrt{3}\sqrt{-1} kvadrat ildizlarining koʻpaytmasi sifatida qayta yozing. Ta’rifi bo‘yicha, -1 ning kvadrat ildizi i ga teng.

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

-i hosil qilish uchun -1 va i ni ko'paytirish.

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

-1 ning kvadrat ildizini hisoblab, i natijaga ega bo‘ling.

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

Faktor: -2=2\left(-1\right). \sqrt{2\left(-1\right)} koʻpaytmasining kvadrat ildizini \sqrt{2}\sqrt{-1} kvadrat ildizlarining koʻpaytmasi sifatida qayta yozing. Ta’rifi bo‘yicha, -1 ning kvadrat ildizi i ga teng.

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

-i hosil qilish uchun -1 va i ni ko'paytirish.

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

Faktor: -3=3\left(-1\right). \sqrt{3\left(-1\right)} koʻpaytmasining kvadrat ildizini \sqrt{3}\sqrt{-1} kvadrat ildizlarining koʻpaytmasi sifatida qayta yozing. Ta’rifi bo‘yicha, -1 ning kvadrat ildizi i ga teng.

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

i+\sqrt{2}i-i\sqrt{3} ifodaning har bir elementini i-i\sqrt{2}+\sqrt{3}i ifodaning har bir elementiga ko‘paytirish orqali taqsimot qonuni xususiyatlarini qo‘llash mumkin.

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

-1 hosil qilish uchun i va i ni ko'paytirish.

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

-1 hosil qilish uchun i va i ni ko'paytirish.

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

0 ni olish uchun \sqrt{2} va -\sqrt{2} ni birlashtirish.

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

\sqrt{2} kvadrati – 2.

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

1 olish uchun -1 va 2'ni qo'shing.

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

\sqrt{3} va \sqrt{2} ni koʻpaytirish uchun kvadrat ildiz ichidagi sonlarni koʻpaytiring.

$$1-\sqrt{3}-\sqrt{6}+\sqrt{3}-\sqrt{3}\sqrt{2}+\left(\sqrt{3}\right)^{2}$$

0 ni olish uchun -\sqrt{3} va \sqrt{3} ni birlashtirish.

$$1-\sqrt{6}-\sqrt{3}\sqrt{2}+\left(\sqrt{3}\right)^{2}$$

\sqrt{3} va \sqrt{2} ni koʻpaytirish uchun kvadrat ildiz ichidagi sonlarni koʻpaytiring.

$$1-\sqrt{6}-\sqrt{6}+\left(\sqrt{3}\right)^{2}$$

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

$$1-2\sqrt{6}+\left(\sqrt{3}\right)^{2}$$

\sqrt{3} kvadrati – 3.

$$1-2\sqrt{6}+3$$

4 olish uchun 1 va 3'ni qo'shing.

$$4-2\sqrt{6}$$

Ashyoviy qism (complex solution)

$$4-2\sqrt{6}$$

Baholash

$$\text{Indeterminate}$$