3x^2+4x^2=7 eching

$$3 x ^ { 2 } + 4 x ^ { 2 } = 7$$

x uchun yechish

$$x=1$$

$$x=-1$$

Kvadratlar farqidan foydalangan qadamlar

7x^{2} ni olish uchun 3x^{2} va 4x^{2} ni birlashtirish.

$$7x^{2}=7$$

Ikkala tarafdan 7 ni ayirish.

$$7x^{2}-7=0$$

Ikki tarafini 7 ga bo‘ling.

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

Hisoblang: x^{2}-1. x^{2}-1 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

7x^{2} ni olish uchun 3x^{2} va 4x^{2} ni birlashtirish.

$$7x^{2}=7$$

Ikki tarafini 7 ga bo‘ling.

$$x^{2}=\frac{7}{7}$$

1 ni olish uchun 7 ni 7 ga bo‘ling.

$$x^{2}=1$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$x=1 x=-1$$

Kvadrat tenglamalaridan foydalanish qoidalari

7x^{2} ni olish uchun 3x^{2} va 4x^{2} ni birlashtirish.

$$7x^{2}=7$$

Ikkala tarafdan 7 ni ayirish.

$$7x^{2}-7=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 7 ni a, 0 ni b va -7 ni c bilan almashtiring.

$$x=\frac{0±\sqrt{0^{2}-4\times 7\left(-7\right)}}{2\times 7}$$

0 kvadratini chiqarish.

$$x=\frac{0±\sqrt{-4\times 7\left(-7\right)}}{2\times 7}$$

-4 ni 7 marotabaga ko'paytirish.

$$x=\frac{0±\sqrt{-28\left(-7\right)}}{2\times 7}$$

-28 ni -7 marotabaga ko'paytirish.

$$x=\frac{0±\sqrt{196}}{2\times 7}$$

196 ning kvadrat ildizini chiqarish.

$$x=\frac{0±14}{2\times 7}$$

2 ni 7 marotabaga ko'paytirish.

$$x=\frac{0±14}{14}$$

x=\frac{0±14}{14} tenglamasini yeching, bunda ± musbat. 14 ni 14 ga bo'lish.

$$x=1$$

x=\frac{0±14}{14} tenglamasini yeching, bunda ± manfiy. -14 ni 14 ga bo'lish.

$$x=-1$$

Tenglama yechildi.

$$x=1 x=-1$$