10^2=2x^2+x^2 eching

$$10 ^ { 2 } = 2 x ^ { 2 } + x ^ { 2 }$$

x uchun yechish

$$x = \frac{10 \sqrt{3}}{3} \approx 5,773502692$$

$$x = -\frac{10 \sqrt{3}}{3} \approx -5,773502692$$

Kvadrat ildizini topish bo'yicha qadamlar

2 daraja ko‘rsatkichini 10 ga hisoblang va 100 ni qiymatni oling.

$$100=2x^{2}+x^{2}$$

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

$$100=3x^{2}$$

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$3x^{2}=100$$

Ikki tarafini 3 ga bo‘ling.

$$x^{2}=\frac{100}{3}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$x=\frac{10\sqrt{3}}{3} x=-\frac{10\sqrt{3}}{3}$$

Kvadrat tenglamalaridan foydalanish qoidalari

2 daraja ko‘rsatkichini 10 ga hisoblang va 100 ni qiymatni oling.

$$100=2x^{2}+x^{2}$$

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

$$100=3x^{2}$$

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$3x^{2}=100$$

Ikkala tarafdan 100 ni ayirish.

$$3x^{2}-100=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 3 ni a, 0 ni b va -100 ni c bilan almashtiring.

$$x=\frac{0±\sqrt{0^{2}-4\times 3\left(-100\right)}}{2\times 3}$$

0 kvadratini chiqarish.

$$x=\frac{0±\sqrt{-4\times 3\left(-100\right)}}{2\times 3}$$

-4 ni 3 marotabaga ko'paytirish.

$$x=\frac{0±\sqrt{-12\left(-100\right)}}{2\times 3}$$

-12 ni -100 marotabaga ko'paytirish.

$$x=\frac{0±\sqrt{1200}}{2\times 3}$$

1200 ning kvadrat ildizini chiqarish.

$$x=\frac{0±20\sqrt{3}}{2\times 3}$$

2 ni 3 marotabaga ko'paytirish.

$$x=\frac{0±20\sqrt{3}}{6}$$

x=\frac{0±20\sqrt{3}}{6} tenglamasini yeching, bunda ± musbat.

$$x=\frac{10\sqrt{3}}{3}$$

x=\frac{0±20\sqrt{3}}{6} tenglamasini yeching, bunda ± manfiy.

$$x=-\frac{10\sqrt{3}}{3}$$

Tenglama yechildi.

$$x=\frac{10\sqrt{3}}{3} x=-\frac{10\sqrt{3}}{3}$$