t^2+3t=3t+4 eching

$$t ^ { 2 } + 3 t = 3 t + 4$$

t uchun yechish

$$t=-2$$

$$t=2$$

Kvadratlar farqidan foydalangan qadamlar

Ikkala tarafdan 3t ni ayirish.

$$t^{2}+3t-3t=4$$

0 ni olish uchun 3t va -3t ni birlashtirish.

$$t^{2}=4$$

Ikkala tarafdan 4 ni ayirish.

$$t^{2}-4=0$$

Hisoblang: t^{2}-4. t^{2}-4 ni t^{2}-2^{2} sifatida qaytadan yozish. Kvadratlarning farqini ushbu formula bilan hisoblash mumkin: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(t-2\right)\left(t+2\right)=0$$

Tenglamani yechish uchun t-2=0 va t+2=0 ni yeching.

$$t=2 t=-2$$

Kvadrat ildizini topish bo'yicha qadamlar

Ikkala tarafdan 3t ni ayirish.

$$t^{2}+3t-3t=4$$

0 ni olish uchun 3t va -3t ni birlashtirish.

$$t^{2}=4$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$t=2 t=-2$$

Kvadrat tenglamalaridan foydalanish qoidalari

Ikkala tarafdan 3t ni ayirish.

$$t^{2}+3t-3t=4$$

0 ni olish uchun 3t va -3t ni birlashtirish.

$$t^{2}=4$$

Ikkala tarafdan 4 ni ayirish.

$$t^{2}-4=0$$

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 -4 ni c bilan almashtiring.

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

0 kvadratini chiqarish.

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

-4 ni -4 marotabaga ko'paytirish.

$$t=\frac{0±\sqrt{16}}{2}$$

16 ning kvadrat ildizini chiqarish.

$$t=\frac{0±4}{2}$$

t=\frac{0±4}{2} tenglamasini yeching, bunda ± musbat. 4 ni 2 ga bo'lish.

$$t=2$$

t=\frac{0±4}{2} tenglamasini yeching, bunda ± manfiy. -4 ni 2 ga bo'lish.

$$t=-2$$

Tenglama yechildi.

$$t=2 t=-2$$