(2x)^2=x^2+9^2 eching

$$( 2 x ) ^ { 2 } = x ^ { 2 } + 9 ^ { 2 }$$

x uchun yechish

$$x=3\sqrt{3}\approx 5,196152423$$

$$x=-3\sqrt{3}\approx -5,196152423$$

Kvadrat ildizini topish bo'yicha qadamlar

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

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

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

$$4x^{2}=x^{2}+9^{2}$$

2 daraja ko‘rsatkichini 9 ga hisoblang va 81 ni qiymatni oling.

$$4x^{2}=x^{2}+81$$

Ikkala tarafdan x^{2} ni ayirish.

$$4x^{2}-x^{2}=81$$

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

$$3x^{2}=81$$

Ikki tarafini 3 ga bo‘ling.

$$x^{2}=\frac{81}{3}$$

27 ni olish uchun 81 ni 3 ga bo‘ling.

$$x^{2}=27$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

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

Kvadrat tenglamalaridan foydalanish qoidalari

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

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

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

$$4x^{2}=x^{2}+9^{2}$$

2 daraja ko‘rsatkichini 9 ga hisoblang va 81 ni qiymatni oling.

$$4x^{2}=x^{2}+81$$

Ikkala tarafdan x^{2} ni ayirish.

$$4x^{2}-x^{2}=81$$

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

$$3x^{2}=81$$

Ikkala tarafdan 81 ni ayirish.

$$3x^{2}-81=0$$

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 -81 ni c bilan almashtiring.

$$x=\frac{0±\sqrt{0^{2}-4\times 3\left(-81\right)}}{2\times 3}$$

0 kvadratini chiqarish.

$$x=\frac{0±\sqrt{-4\times 3\left(-81\right)}}{2\times 3}$$

-4 ni 3 marotabaga ko'paytirish.

$$x=\frac{0±\sqrt{-12\left(-81\right)}}{2\times 3}$$

-12 ni -81 marotabaga ko'paytirish.

$$x=\frac{0±\sqrt{972}}{2\times 3}$$

972 ning kvadrat ildizini chiqarish.

$$x=\frac{0±18\sqrt{3}}{2\times 3}$$

2 ni 3 marotabaga ko'paytirish.

$$x=\frac{0±18\sqrt{3}}{6}$$

x=\frac{0±18\sqrt{3}}{6} tenglamasini yeching, bunda ± musbat.

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

x=\frac{0±18\sqrt{3}}{6} tenglamasini yeching, bunda ± manfiy.

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

Tenglama yechildi.

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