xsqrt{457}*35=sqrt{x^2+2} eching

$$x \sqrt{ 457 } \times 35= \sqrt{ { x }^{ 2 } +2 }$$

x uchun yechish

$$x=\frac{\sqrt{69978}}{139956}\approx 0,001890119$$

Yechim qadamlari

Tenglamaning ikkala taraf kvadratini chiqarish.

$$\left(35x\sqrt{457}\right)^{2}=\left(\sqrt{x^{2}+2}\right)^{2}$$

\left(35x\sqrt{457}\right)^{2} ni kengaytirish.

$$35^{2}x^{2}\left(\sqrt{457}\right)^{2}=\left(\sqrt{x^{2}+2}\right)^{2}$$

2 daraja ko‘rsatkichini 35 ga hisoblang va 1225 ni qiymatni oling.

$$1225x^{2}\left(\sqrt{457}\right)^{2}=\left(\sqrt{x^{2}+2}\right)^{2}$$

\sqrt{457} kvadrati – 457.

$$1225x^{2}\times 457=\left(\sqrt{x^{2}+2}\right)^{2}$$

559825 hosil qilish uchun 1225 va 457 ni ko'paytirish.

$$559825x^{2}=\left(\sqrt{x^{2}+2}\right)^{2}$$

2 daraja ko‘rsatkichini \sqrt{x^{2}+2} ga hisoblang va x^{2}+2 ni qiymatni oling.

$$559825x^{2}=x^{2}+2$$

Ikkala tarafdan x^{2} ni ayirish.

$$559825x^{2}-x^{2}=2$$

559824x^{2} ni olish uchun 559825x^{2} va -x^{2} ni birlashtirish.

$$559824x^{2}=2$$

Ikki tarafini 559824 ga bo‘ling.

$$x^{2}=\frac{2}{559824}$$

\frac{2}{559824} ulushini 2 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$x^{2}=\frac{1}{279912}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$x=\frac{\sqrt{69978}}{139956} x=-\frac{\sqrt{69978}}{139956}$$

35x\sqrt{457}=\sqrt{x^{2}+2} tenglamasida x uchun \frac{\sqrt{69978}}{139956} ni almashtiring.

$$35\times \frac{\sqrt{69978}}{139956}\sqrt{457}=\sqrt{\left(\frac{\sqrt{69978}}{139956}\right)^{2}+2}$$

Qisqartirish. x=\frac{\sqrt{69978}}{139956} tenglamani qoniqtiradi.

$$\frac{35}{139956}\times 31979946^{\frac{1}{2}}=\frac{35}{139956}\times 31979946^{\frac{1}{2}}$$

35x\sqrt{457}=\sqrt{x^{2}+2} tenglamasida x uchun -\frac{\sqrt{69978}}{139956} ni almashtiring.

$$35\left(-\frac{\sqrt{69978}}{139956}\right)\sqrt{457}=\sqrt{\left(-\frac{\sqrt{69978}}{139956}\right)^{2}+2}$$

Qisqartirish. x=-\frac{\sqrt{69978}}{139956} qiymati bu tenglamani qoniqtirmaydi, chunki oʻng va chap tarafdagi belgilar bir-biriga qarama-qarshi.

$$-\frac{35}{139956}\times 31979946^{\frac{1}{2}}=\frac{35}{139956}\times 31979946^{\frac{1}{2}}$$

35\sqrt{457}x=\sqrt{x^{2}+2} tenglamasi noyob yechimga ega.

$$x=\frac{\sqrt{69978}}{139956}$$