x^2=(2+sqrt{5})^2+(2-sqrt{5})^2 eching

$$x ^ { 2 } = ( 2 + \sqrt { 5 } ) ^ { 2 } + ( 2 - \sqrt { 5 } ) ^ { 2 }$$

x uchun yechish

$$x=3\sqrt{2}\approx 4,242640687$$

$$x=-3\sqrt{2}\approx -4,242640687$$

Kvadrat ildizini topish bo'yicha qadamlar

\left(a+b\right)^{2}=a^{2}+2ab+b^{2} binom teoremasini \left(2+\sqrt{5}\right)^{2} kengaytirilishi uchun ishlating.

$$x^{2}=4+4\sqrt{5}+\left(\sqrt{5}\right)^{2}+\left(2-\sqrt{5}\right)^{2}$$

\sqrt{5} kvadrati – 5.

$$x^{2}=4+4\sqrt{5}+5+\left(2-\sqrt{5}\right)^{2}$$

9 olish uchun 4 va 5'ni qo'shing.

$$x^{2}=9+4\sqrt{5}+\left(2-\sqrt{5}\right)^{2}$$

\left(a-b\right)^{2}=a^{2}-2ab+b^{2} binom teoremasini \left(2-\sqrt{5}\right)^{2} kengaytirilishi uchun ishlating.

$$x^{2}=9+4\sqrt{5}+4-4\sqrt{5}+\left(\sqrt{5}\right)^{2}$$

\sqrt{5} kvadrati – 5.

$$x^{2}=9+4\sqrt{5}+4-4\sqrt{5}+5$$

9 olish uchun 4 va 5'ni qo'shing.

$$x^{2}=9+4\sqrt{5}+9-4\sqrt{5}$$

18 olish uchun 9 va 9'ni qo'shing.

$$x^{2}=18+4\sqrt{5}-4\sqrt{5}$$

0 ni olish uchun 4\sqrt{5} va -4\sqrt{5} ni birlashtirish.

$$x^{2}=18$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$x=3\sqrt{2} x=-3\sqrt{2}$$

Kvadrat tenglamalaridan foydalanish qoidalari

\left(a+b\right)^{2}=a^{2}+2ab+b^{2} binom teoremasini \left(2+\sqrt{5}\right)^{2} kengaytirilishi uchun ishlating.

$$x^{2}=4+4\sqrt{5}+\left(\sqrt{5}\right)^{2}+\left(2-\sqrt{5}\right)^{2}$$

\sqrt{5} kvadrati – 5.

$$x^{2}=4+4\sqrt{5}+5+\left(2-\sqrt{5}\right)^{2}$$

9 olish uchun 4 va 5'ni qo'shing.

$$x^{2}=9+4\sqrt{5}+\left(2-\sqrt{5}\right)^{2}$$

\left(a-b\right)^{2}=a^{2}-2ab+b^{2} binom teoremasini \left(2-\sqrt{5}\right)^{2} kengaytirilishi uchun ishlating.

$$x^{2}=9+4\sqrt{5}+4-4\sqrt{5}+\left(\sqrt{5}\right)^{2}$$

\sqrt{5} kvadrati – 5.

$$x^{2}=9+4\sqrt{5}+4-4\sqrt{5}+5$$

9 olish uchun 4 va 5'ni qo'shing.

$$x^{2}=9+4\sqrt{5}+9-4\sqrt{5}$$

18 olish uchun 9 va 9'ni qo'shing.

$$x^{2}=18+4\sqrt{5}-4\sqrt{5}$$

0 ni olish uchun 4\sqrt{5} va -4\sqrt{5} ni birlashtirish.

$$x^{2}=18$$

Ikkala tarafdan 18 ni ayirish.

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

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 1 ni a, 0 ni b va -18 ni c bilan almashtiring.

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

0 kvadratini chiqarish.

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

-4 ni -18 marotabaga ko'paytirish.

$$x=\frac{0±\sqrt{72}}{2}$$

72 ning kvadrat ildizini chiqarish.

$$x=\frac{0±6\sqrt{2}}{2}$$

x=\frac{0±6\sqrt{2}}{2} tenglamasini yeching, bunda ± musbat.

$$x=3\sqrt{2}$$

x=\frac{0±6\sqrt{2}}{2} tenglamasini yeching, bunda ± manfiy.

$$x=-3\sqrt{2}$$

Tenglama yechildi.

$$x=3\sqrt{2} x=-3\sqrt{2}$$