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

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

x uchun yechish

$$x=2$$

$$x=-2$$

Kvadratlar farqidan foydalangan qadamlar

Tenglamaning ikkala tarafini 3 ga ko'paytirish.

$$3\times \left(2\sqrt{2}\right)^{2}=3\left(\left(\sqrt{3}x\right)^{2}+x^{2}\right)-2\sqrt{3}xx\sqrt{3}$$

3 hosil qilish uchun \sqrt{3} va \sqrt{3} ni ko'paytirish.

$$3\times \left(2\sqrt{2}\right)^{2}=3\left(\left(\sqrt{3}x\right)^{2}+x^{2}\right)-2\times 3xx$$

x^{2} hosil qilish uchun x va x ni ko'paytirish.

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

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

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

2 daraja ko‘rsatkichini 2 ga hisoblang va 4 ni qiymatni oling.

$$3\times 4\left(\sqrt{2}\right)^{2}=3\left(\left(\sqrt{3}x\right)^{2}+x^{2}\right)-2\times 3x^{2}$$

\sqrt{2} kvadrati – 2.

$$3\times 4\times 2=3\left(\left(\sqrt{3}x\right)^{2}+x^{2}\right)-2\times 3x^{2}$$

8 hosil qilish uchun 4 va 2 ni ko'paytirish.

$$3\times 8=3\left(\left(\sqrt{3}x\right)^{2}+x^{2}\right)-2\times 3x^{2}$$

24 hosil qilish uchun 3 va 8 ni ko'paytirish.

$$24=3\left(\left(\sqrt{3}x\right)^{2}+x^{2}\right)-2\times 3x^{2}$$

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

$$24=3\left(\left(\sqrt{3}\right)^{2}x^{2}+x^{2}\right)-2\times 3x^{2}$$

\sqrt{3} kvadrati – 3.

$$24=3\left(3x^{2}+x^{2}\right)-2\times 3x^{2}$$

4x^{2} ni olish uchun 3x^{2} va x^{2} ni birlashtirish.

$$24=3\times 4x^{2}-2\times 3x^{2}$$

12 hosil qilish uchun 3 va 4 ni ko'paytirish.

$$24=12x^{2}-2\times 3x^{2}$$

6 hosil qilish uchun 2 va 3 ni ko'paytirish.

$$24=12x^{2}-6x^{2}$$

6x^{2} ni olish uchun 12x^{2} va -6x^{2} ni birlashtirish.

$$24=6x^{2}$$

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$6x^{2}=24$$

Ikkala tarafdan 24 ni ayirish.

$$6x^{2}-24=0$$

Ikki tarafini 6 ga bo‘ling.

$$x^{2}-4=0$$

Hisoblang: x^{2}-4. x^{2}-4 ni x^{2}-2^{2} sifatida qaytadan yozish. Kvadratlarning farqini ushbu formula bilan hisoblash mumkin: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(x-2\right)\left(x+2\right)=0$$

Tenglamani yechish uchun x-2=0 va x+2=0 ni yeching.

$$x=2 x=-2$$

Kvadrat ildizini topish bo'yicha qadamlar

Tenglamaning ikkala tarafini 3 ga ko'paytirish.

$$3\times \left(2\sqrt{2}\right)^{2}=3\left(\left(\sqrt{3}x\right)^{2}+x^{2}\right)-2\sqrt{3}xx\sqrt{3}$$

3 hosil qilish uchun \sqrt{3} va \sqrt{3} ni ko'paytirish.

$$3\times \left(2\sqrt{2}\right)^{2}=3\left(\left(\sqrt{3}x\right)^{2}+x^{2}\right)-2\times 3xx$$

x^{2} hosil qilish uchun x va x ni ko'paytirish.

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

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

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

2 daraja ko‘rsatkichini 2 ga hisoblang va 4 ni qiymatni oling.

$$3\times 4\left(\sqrt{2}\right)^{2}=3\left(\left(\sqrt{3}x\right)^{2}+x^{2}\right)-2\times 3x^{2}$$

\sqrt{2} kvadrati – 2.

$$3\times 4\times 2=3\left(\left(\sqrt{3}x\right)^{2}+x^{2}\right)-2\times 3x^{2}$$

8 hosil qilish uchun 4 va 2 ni ko'paytirish.

$$3\times 8=3\left(\left(\sqrt{3}x\right)^{2}+x^{2}\right)-2\times 3x^{2}$$

24 hosil qilish uchun 3 va 8 ni ko'paytirish.

$$24=3\left(\left(\sqrt{3}x\right)^{2}+x^{2}\right)-2\times 3x^{2}$$

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

$$24=3\left(\left(\sqrt{3}\right)^{2}x^{2}+x^{2}\right)-2\times 3x^{2}$$

\sqrt{3} kvadrati – 3.

$$24=3\left(3x^{2}+x^{2}\right)-2\times 3x^{2}$$

4x^{2} ni olish uchun 3x^{2} va x^{2} ni birlashtirish.

$$24=3\times 4x^{2}-2\times 3x^{2}$$

12 hosil qilish uchun 3 va 4 ni ko'paytirish.

$$24=12x^{2}-2\times 3x^{2}$$

6 hosil qilish uchun 2 va 3 ni ko'paytirish.

$$24=12x^{2}-6x^{2}$$

6x^{2} ni olish uchun 12x^{2} va -6x^{2} ni birlashtirish.

$$24=6x^{2}$$

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$6x^{2}=24$$

Ikki tarafini 6 ga bo‘ling.

$$x^{2}=\frac{24}{6}$$

4 ni olish uchun 24 ni 6 ga bo‘ling.

$$x^{2}=4$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$x=2 x=-2$$

Kvadrat tenglamalaridan foydalanish qoidalari

Tenglamaning ikkala tarafini 3 ga ko'paytirish.

$$3\times \left(2\sqrt{2}\right)^{2}=3\left(\left(\sqrt{3}x\right)^{2}+x^{2}\right)-2\sqrt{3}xx\sqrt{3}$$

3 hosil qilish uchun \sqrt{3} va \sqrt{3} ni ko'paytirish.

$$3\times \left(2\sqrt{2}\right)^{2}=3\left(\left(\sqrt{3}x\right)^{2}+x^{2}\right)-2\times 3xx$$

x^{2} hosil qilish uchun x va x ni ko'paytirish.

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

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

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

2 daraja ko‘rsatkichini 2 ga hisoblang va 4 ni qiymatni oling.

$$3\times 4\left(\sqrt{2}\right)^{2}=3\left(\left(\sqrt{3}x\right)^{2}+x^{2}\right)-2\times 3x^{2}$$

\sqrt{2} kvadrati – 2.

$$3\times 4\times 2=3\left(\left(\sqrt{3}x\right)^{2}+x^{2}\right)-2\times 3x^{2}$$

8 hosil qilish uchun 4 va 2 ni ko'paytirish.

$$3\times 8=3\left(\left(\sqrt{3}x\right)^{2}+x^{2}\right)-2\times 3x^{2}$$

24 hosil qilish uchun 3 va 8 ni ko'paytirish.

$$24=3\left(\left(\sqrt{3}x\right)^{2}+x^{2}\right)-2\times 3x^{2}$$

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

$$24=3\left(\left(\sqrt{3}\right)^{2}x^{2}+x^{2}\right)-2\times 3x^{2}$$

\sqrt{3} kvadrati – 3.

$$24=3\left(3x^{2}+x^{2}\right)-2\times 3x^{2}$$

4x^{2} ni olish uchun 3x^{2} va x^{2} ni birlashtirish.

$$24=3\times 4x^{2}-2\times 3x^{2}$$

12 hosil qilish uchun 3 va 4 ni ko'paytirish.

$$24=12x^{2}-2\times 3x^{2}$$

6 hosil qilish uchun 2 va 3 ni ko'paytirish.

$$24=12x^{2}-6x^{2}$$

6x^{2} ni olish uchun 12x^{2} va -6x^{2} ni birlashtirish.

$$24=6x^{2}$$

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$6x^{2}=24$$

Ikkala tarafdan 24 ni ayirish.

$$6x^{2}-24=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 6 ni a, 0 ni b va -24 ni c bilan almashtiring.

$$x=\frac{0±\sqrt{0^{2}-4\times 6\left(-24\right)}}{2\times 6}$$

0 kvadratini chiqarish.

$$x=\frac{0±\sqrt{-4\times 6\left(-24\right)}}{2\times 6}$$

-4 ni 6 marotabaga ko'paytirish.

$$x=\frac{0±\sqrt{-24\left(-24\right)}}{2\times 6}$$

-24 ni -24 marotabaga ko'paytirish.

$$x=\frac{0±\sqrt{576}}{2\times 6}$$

576 ning kvadrat ildizini chiqarish.

$$x=\frac{0±24}{2\times 6}$$

2 ni 6 marotabaga ko'paytirish.

$$x=\frac{0±24}{12}$$

x=\frac{0±24}{12} tenglamasini yeching, bunda ± musbat. 24 ni 12 ga bo'lish.

$$x=2$$

x=\frac{0±24}{12} tenglamasini yeching, bunda ± manfiy. -24 ni 12 ga bo'lish.

$$x=-2$$

Tenglama yechildi.

$$x=2 x=-2$$