x^2+x^2=(3sqrt{2})^2 eching

$$x ^ { 2 } + x ^ { 2 } = ( 3 \sqrt { 2 } ) ^ { 2 }$$

x uchun yechish

$$x=3$$

$$x=-3$$

Kvadratlar farqidan foydalangan qadamlar

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

$$2x^{2}=\left(3\sqrt{2}\right)^{2}$$

\left(3\sqrt{2}\right)^{2} ni kengaytirish.

$$2x^{2}=3^{2}\left(\sqrt{2}\right)^{2}$$

2 daraja ko‘rsatkichini 3 ga hisoblang va 9 ni qiymatni oling.

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

\sqrt{2} kvadrati – 2.

$$2x^{2}=9\times 2$$

18 hosil qilish uchun 9 va 2 ni ko'paytirish.

$$2x^{2}=18$$

Ikkala tarafdan 18 ni ayirish.

$$2x^{2}-18=0$$

Ikki tarafini 2 ga bo‘ling.

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

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.

$$x=3 x=-3$$

Kvadrat ildizini topish bo'yicha qadamlar

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

$$2x^{2}=\left(3\sqrt{2}\right)^{2}$$

\left(3\sqrt{2}\right)^{2} ni kengaytirish.

$$2x^{2}=3^{2}\left(\sqrt{2}\right)^{2}$$

2 daraja ko‘rsatkichini 3 ga hisoblang va 9 ni qiymatni oling.

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

\sqrt{2} kvadrati – 2.

$$2x^{2}=9\times 2$$

18 hosil qilish uchun 9 va 2 ni ko'paytirish.

$$2x^{2}=18$$

Ikki tarafini 2 ga bo‘ling.

$$x^{2}=\frac{18}{2}$$

9 ni olish uchun 18 ni 2 ga bo‘ling.

$$x^{2}=9$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$x=3 x=-3$$

Kvadrat tenglamalaridan foydalanish qoidalari

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

$$2x^{2}=\left(3\sqrt{2}\right)^{2}$$

\left(3\sqrt{2}\right)^{2} ni kengaytirish.

$$2x^{2}=3^{2}\left(\sqrt{2}\right)^{2}$$

2 daraja ko‘rsatkichini 3 ga hisoblang va 9 ni qiymatni oling.

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

\sqrt{2} kvadrati – 2.

$$2x^{2}=9\times 2$$

18 hosil qilish uchun 9 va 2 ni ko'paytirish.

$$2x^{2}=18$$

Ikkala tarafdan 18 ni ayirish.

$$2x^{2}-18=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 2 ni a, 0 ni b va -18 ni c bilan almashtiring.

$$x=\frac{0±\sqrt{0^{2}-4\times 2\left(-18\right)}}{2\times 2}$$

0 kvadratini chiqarish.

$$x=\frac{0±\sqrt{-4\times 2\left(-18\right)}}{2\times 2}$$

-4 ni 2 marotabaga ko'paytirish.

$$x=\frac{0±\sqrt{-8\left(-18\right)}}{2\times 2}$$

-8 ni -18 marotabaga ko'paytirish.

$$x=\frac{0±\sqrt{144}}{2\times 2}$$

144 ning kvadrat ildizini chiqarish.

$$x=\frac{0±12}{2\times 2}$$

2 ni 2 marotabaga ko'paytirish.

$$x=\frac{0±12}{4}$$

x=\frac{0±12}{4} tenglamasini yeching, bunda ± musbat. 12 ni 4 ga bo'lish.

$$x=3$$

x=\frac{0±12}{4} tenglamasini yeching, bunda ± manfiy. -12 ni 4 ga bo'lish.

$$x=-3$$

Tenglama yechildi.

$$x=3 x=-3$$