sqrt{x}+sqrt{x+7}=17 eching

$$\sqrt { x } + \sqrt { x + 7 } = 17$$

x uchun yechish

$$x = \frac{19881}{289} = 68\frac{229}{289} \approx 68,792387543$$

Yechim qadamlari

Tenglamaning ikkala tarafidan \sqrt{x+7} ni ayirish.

$$\sqrt{x}=17-\sqrt{x+7}$$

Tenglamaning ikkala taraf kvadratini chiqarish.

$$\left(\sqrt{x}\right)^{2}=\left(17-\sqrt{x+7}\right)^{2}$$

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

$$x=\left(17-\sqrt{x+7}\right)^{2}$$

\left(a-b\right)^{2}=a^{2}-2ab+b^{2} binom teoremasini \left(17-\sqrt{x+7}\right)^{2} kengaytirilishi uchun ishlating.

$$x=289-34\sqrt{x+7}+\left(\sqrt{x+7}\right)^{2}$$

2 daraja ko‘rsatkichini \sqrt{x+7} ga hisoblang va x+7 ni qiymatni oling.

$$x=289-34\sqrt{x+7}+x+7$$

296 olish uchun 289 va 7'ni qo'shing.

$$x=296-34\sqrt{x+7}+x$$

34\sqrt{x+7} ni ikki tarafga qo’shing.

$$x+34\sqrt{x+7}=296+x$$

Ikkala tarafdan x ni ayirish.

$$x+34\sqrt{x+7}-x=296$$

0 ni olish uchun x va -x ni birlashtirish.

$$34\sqrt{x+7}=296$$

Ikki tarafini 34 ga bo‘ling.

$$\sqrt{x+7}=\frac{296}{34}$$

\frac{296}{34} ulushini 2 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$\sqrt{x+7}=\frac{148}{17}$$

Tenglamaning ikkala taraf kvadratini chiqarish.

$$x+7=\frac{21904}{289}$$

Tenglamaning ikkala tarafidan 7 ni ayirish.

$$x+7-7=\frac{21904}{289}-7$$

O‘zidan 7 ayirilsa 0 qoladi.

$$x=\frac{21904}{289}-7$$

\frac{21904}{289} dan 7 ni ayirish.

$$x=\frac{19881}{289}$$

\sqrt{x}+\sqrt{x+7}=17 tenglamasida x uchun \frac{19881}{289} ni almashtiring.

$$\sqrt{\frac{19881}{289}}+\sqrt{\frac{19881}{289}+7}=17$$

Qisqartirish. x=\frac{19881}{289} tenglamani qoniqtiradi.

$$17=17$$

\sqrt{x}=-\sqrt{x+7}+17 tenglamasi noyob yechimga ega.

$$x=\frac{19881}{289}$$