80=x+sqrt{36+x^2} eching

$$80 = x + \sqrt { 36 + x ^ { 2 } }$$

x uchun yechish

$$x = \frac{1591}{40} = 39\frac{31}{40} = 39,775$$

Yechim qadamlari

Tenglamaning ikkala tarafidan x ni ayirish.

$$80-x=\sqrt{36+x^{2}}$$

Tenglamaning ikkala taraf kvadratini chiqarish.

$$\left(80-x\right)^{2}=\left(\sqrt{36+x^{2}}\right)^{2}$$

\left(a-b\right)^{2}=a^{2}-2ab+b^{2} binom teoremasini \left(80-x\right)^{2} kengaytirilishi uchun ishlating.

$$6400-160x+x^{2}=\left(\sqrt{36+x^{2}}\right)^{2}$$

2 daraja ko‘rsatkichini \sqrt{36+x^{2}} ga hisoblang va 36+x^{2} ni qiymatni oling.

$$6400-160x+x^{2}=36+x^{2}$$

Ikkala tarafdan x^{2} ni ayirish.

$$6400-160x+x^{2}-x^{2}=36$$

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

$$6400-160x=36$$

Ikkala tarafdan 6400 ni ayirish.

$$-160x=36-6400$$

-6364 olish uchun 36 dan 6400 ni ayirish.

$$-160x=-6364$$

Ikki tarafini -160 ga bo‘ling.

$$x=\frac{-6364}{-160}$$

\frac{-6364}{-160} ulushini -4 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$x=\frac{1591}{40}$$

80=x+\sqrt{36+x^{2}} tenglamasida x uchun \frac{1591}{40} ni almashtiring.

$$80=\frac{1591}{40}+\sqrt{36+\left(\frac{1591}{40}\right)^{2}}$$

Qisqartirish. x=\frac{1591}{40} tenglamani qoniqtiradi.

$$80=80$$

80-x=\sqrt{x^{2}+36} tenglamasi noyob yechimga ega.

$$x=\frac{1591}{40}$$