(2x)^2-2x(-x)-3=-1 eching

$$( 2 x ) ^ { 2 } - 2 x ( - x ) - 3 = - 1$$

x uchun yechish

$$x=\frac{\sqrt{3}}{3}\approx 0,577350269$$

$$x=-\frac{\sqrt{3}}{3}\approx -0,577350269$$

Kvadrat ildizini topish bo'yicha qadamlar

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

$$2^{2}x^{2}-2x\left(-x\right)-3=-1$$

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

$$4x^{2}-2x\left(-x\right)-3=-1$$

3 ni ikki tarafga qo’shing.

$$4x^{2}-2x\left(-x\right)=-1+3$$

2 olish uchun -1 va 3'ni qo'shing.

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

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

$$4x^{2}-2x^{2}\left(-1\right)=2$$

2 hosil qilish uchun -2 va -1 ni ko'paytirish.

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

6x^{2} ni olish uchun 4x^{2} va 2x^{2} ni birlashtirish.

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

Ikki tarafini 6 ga bo‘ling.

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

\frac{2}{6} ulushini 2 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$x^{2}=\frac{1}{3}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

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

Kvadrat tenglamalaridan foydalanish qoidalari

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

$$2^{2}x^{2}-2x\left(-x\right)-3=-1$$

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

$$4x^{2}-2x\left(-x\right)-3=-1$$

1 ni ikki tarafga qo’shing.

$$4x^{2}-2x\left(-x\right)-3+1=0$$

-2 olish uchun -3 va 1'ni qo'shing.

$$4x^{2}-2x\left(-x\right)-2=0$$

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

$$4x^{2}-2x^{2}\left(-1\right)-2=0$$

2 hosil qilish uchun -2 va -1 ni ko'paytirish.

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

6x^{2} ni olish uchun 4x^{2} va 2x^{2} ni birlashtirish.

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

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 -2 ni c bilan almashtiring.

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

0 kvadratini chiqarish.

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

-4 ni 6 marotabaga ko'paytirish.

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

-24 ni -2 marotabaga ko'paytirish.

$$x=\frac{0±\sqrt{48}}{2\times 6}$$

48 ning kvadrat ildizini chiqarish.

$$x=\frac{0±4\sqrt{3}}{2\times 6}$$

2 ni 6 marotabaga ko'paytirish.

$$x=\frac{0±4\sqrt{3}}{12}$$

x=\frac{0±4\sqrt{3}}{12} tenglamasini yeching, bunda ± musbat.

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

x=\frac{0±4\sqrt{3}}{12} tenglamasini yeching, bunda ± manfiy.

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

Tenglama yechildi.

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