3-4x^2=5-6x^2 eching

$$3 - 4 x ^ { 2 } = 5 - 6 x ^ { 2 }$$

x uchun yechish

$$x=1$$

$$x=-1$$

Kvadratlar farqidan foydalangan qadamlar

Ikkala tarafdan 5 ni ayirish.

$$3-4x^{2}-5=-6x^{2}$$

-2 olish uchun 3 dan 5 ni ayirish.

$$-2-4x^{2}=-6x^{2}$$

6x^{2} ni ikki tarafga qo’shing.

$$-2-4x^{2}+6x^{2}=0$$

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

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

Ikki tarafini 2 ga bo‘ling.

$$-1+x^{2}=0$$

Hisoblang: -1+x^{2}. -1+x^{2} ni x^{2}-1^{2} sifatida qaytadan yozish. Kvadratlarning farqini ushbu formula bilan hisoblash mumkin: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(x-1\right)\left(x+1\right)=0$$

Tenglamani yechish uchun x-1=0 va x+1=0 ni yeching.

$$x=1 x=-1$$

Kvadrat ildizini topish bo'yicha qadamlar

6x^{2} ni ikki tarafga qo’shing.

$$3-4x^{2}+6x^{2}=5$$

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

$$3+2x^{2}=5$$

Ikkala tarafdan 3 ni ayirish.

$$2x^{2}=5-3$$

2 olish uchun 5 dan 3 ni ayirish.

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

Ikki tarafini 2 ga bo‘ling.

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

1 ni olish uchun 2 ni 2 ga bo‘ling.

$$x^{2}=1$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$x=1 x=-1$$

Kvadrat tenglamalaridan foydalanish qoidalari

Ikkala tarafdan 5 ni ayirish.

$$3-4x^{2}-5=-6x^{2}$$

-2 olish uchun 3 dan 5 ni ayirish.

$$-2-4x^{2}=-6x^{2}$$

6x^{2} ni ikki tarafga qo’shing.

$$-2-4x^{2}+6x^{2}=0$$

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

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

Bu kabi kvadrat tenglamalarni x^{2} sharti bilan, biroq x shartisiz hamon kvadrat tenglamasidan foydalanib yechish mumkin, \frac{-b±\sqrt{b^{2}-4ac}}{2a}, ular standart formulaga solingandan so'ng: ax^{2}+bx+c=0.

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

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

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

0 kvadratini chiqarish.

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

-4 ni 2 marotabaga ko'paytirish.

$$x=\frac{0±\sqrt{-8\left(-2\right)}}{2\times 2}$$

-8 ni -2 marotabaga ko'paytirish.

$$x=\frac{0±\sqrt{16}}{2\times 2}$$

16 ning kvadrat ildizini chiqarish.

$$x=\frac{0±4}{2\times 2}$$

2 ni 2 marotabaga ko'paytirish.

$$x=\frac{0±4}{4}$$

x=\frac{0±4}{4} tenglamasini yeching, bunda ± musbat. 4 ni 4 ga bo'lish.

$$x=1$$

x=\frac{0±4}{4} tenglamasini yeching, bunda ± manfiy. -4 ni 4 ga bo'lish.

$$x=-1$$

Tenglama yechildi.

$$x=1 x=-1$$