sqrt{2x^2-9}-x=0 eching

$$\sqrt { 2 x ^ { 2 } - 9 } - x = 0$$

x uchun yechish

$$x=3$$

Yechim qadamlari

Tenglamaning ikkala tarafidan -x ni ayirish.

$$\sqrt{2x^{2}-9}=x$$

Tenglamaning ikkala taraf kvadratini chiqarish.

$$\left(\sqrt{2x^{2}-9}\right)^{2}=x^{2}$$

2 daraja ko‘rsatkichini \sqrt{2x^{2}-9} ga hisoblang va 2x^{2}-9 ni qiymatni oling.

$$2x^{2}-9=x^{2}$$

Ikkala tarafdan x^{2} ni ayirish.

$$2x^{2}-9-x^{2}=0$$

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

$$x^{2}-9=0$$

Hisoblang: x^{2}-9. x^{2}-9 ni x^{2}-3^{2} sifatida qaytadan yozish. Kvadratlarning farqini ushbu formula bilan hisoblash mumkin: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(x-3\right)\left(x+3\right)=0$$

Tenglamani yechish uchun x-3=0 va x+3=0 ni yeching.

$$x=3 x=-3$$

\sqrt{2x^{2}-9}-x=0 tenglamasida x uchun 3 ni almashtiring.

$$\sqrt{2\times 3^{2}-9}-3=0$$

Qisqartirish. x=3 tenglamani qoniqtiradi.

$$0=0$$

\sqrt{2x^{2}-9}-x=0 tenglamasida x uchun -3 ni almashtiring.

$$\sqrt{2\left(-3\right)^{2}-9}-\left(-3\right)=0$$

Qisqartirish. x=-3 qiymati bu tenglamani qoniqtirmaydi.

$$6=0$$

\sqrt{2x^{2}-9}=x tenglamasi noyob yechimga ega.

$$x=3$$