t^2+4t+1=3 eching

$$t ^ { 2 } + 4 t + 1 = 3$$

t uchun yechish

$$t=\sqrt{6}-2\approx 0,449489743$$

$$t=-\sqrt{6}-2\approx -4,449489743$$

Kvadrat tenglamalaridan foydalanish qoidalari

ax^{2}+bx+c=0 shaklidagi barcha tenglamalarni kvadrat formulasi bilan yechish mumkin: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. Kvadrat formula ikki yechmni taqdim qiladi, biri ± qo'shish bo'lganda, va ikkinchisi ayiruv bo'lganda.

$$t^{2}+4t+1=3$$

Tenglamaning ikkala tarafidan 3 ni ayirish.

$$t^{2}+4t+1-3=3-3$$

O‘zidan 3 ayirilsa 0 qoladi.

$$t^{2}+4t+1-3=0$$

1 dan 3 ni ayirish.

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

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

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

4 kvadratini chiqarish.

$$t=\frac{-4±\sqrt{16-4\left(-2\right)}}{2}$$

-4 ni -2 marotabaga ko'paytirish.

$$t=\frac{-4±\sqrt{16+8}}{2}$$

16 ni 8 ga qo'shish.

$$t=\frac{-4±\sqrt{24}}{2}$$

24 ning kvadrat ildizini chiqarish.

$$t=\frac{-4±2\sqrt{6}}{2}$$

t=\frac{-4±2\sqrt{6}}{2} tenglamasini yeching, bunda ± musbat. -4 ni 2\sqrt{6} ga qo'shish.

$$t=\frac{2\sqrt{6}-4}{2}$$

-4+2\sqrt{6} ni 2 ga bo'lish.

$$t=\sqrt{6}-2$$

t=\frac{-4±2\sqrt{6}}{2} tenglamasini yeching, bunda ± manfiy. -4 dan 2\sqrt{6} ni ayirish.

$$t=\frac{-2\sqrt{6}-4}{2}$$

-4-2\sqrt{6} ni 2 ga bo'lish.

$$t=-\sqrt{6}-2$$

Tenglama yechildi.

$$t=\sqrt{6}-2 t=-\sqrt{6}-2$$

Kvadratni yakunlash bo'yicha qadamlar

Bu kabi kvadrat tenglamalarni kvadratni yakunlab yechish mumkin. Kvadratni yechish uchun tenglama avval ushbu shaklda bo'lishi shart: x^{2}+bx=c.

$$t^{2}+4t+1=3$$

Tenglamaning ikkala tarafidan 1 ni ayirish.

$$t^{2}+4t+1-1=3-1$$

O‘zidan 1 ayirilsa 0 qoladi.

$$t^{2}+4t=3-1$$

3 dan 1 ni ayirish.

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

4 ni bo‘lish, x shartining koeffitsienti, 2 ga 2 olish uchun. Keyin, 2 ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

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

2 kvadratini chiqarish.

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

2 ni 4 ga qo'shish.

$$t^{2}+4t+4=6$$

t^{2}+4t+4 omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(t+2\right)^{2}=6$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(t+2\right)^{2}}=\sqrt{6}$$

Qisqartirish.

$$t+2=\sqrt{6} t+2=-\sqrt{6}$$

Tenglamaning ikkala tarafidan 2 ni ayirish.

$$t=\sqrt{6}-2 t=-\sqrt{6}-2$$