t^2-8t-5=0 eching

$$t ^ { 2 } - 8 t - 5 = 0$$

t uchun yechish

$$t=\sqrt{21}+4\approx 8,582575695$$

$$t=4-\sqrt{21}\approx -0,582575695$$

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.

$$t^{2}-8t-5=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 1 ni a, -8 ni b va -5 ni c bilan almashtiring.

$$t=\frac{-\left(-8\right)±\sqrt{\left(-8\right)^{2}-4\left(-5\right)}}{2}$$

-8 kvadratini chiqarish.

$$t=\frac{-\left(-8\right)±\sqrt{64-4\left(-5\right)}}{2}$$

-4 ni -5 marotabaga ko'paytirish.

$$t=\frac{-\left(-8\right)±\sqrt{64+20}}{2}$$

64 ni 20 ga qo'shish.

$$t=\frac{-\left(-8\right)±\sqrt{84}}{2}$$

84 ning kvadrat ildizini chiqarish.

$$t=\frac{-\left(-8\right)±2\sqrt{21}}{2}$$

-8 ning teskarisi 8 ga teng.

$$t=\frac{8±2\sqrt{21}}{2}$$

t=\frac{8±2\sqrt{21}}{2} tenglamasini yeching, bunda ± musbat. 8 ni 2\sqrt{21} ga qo'shish.

$$t=\frac{2\sqrt{21}+8}{2}$$

8+2\sqrt{21} ni 2 ga bo'lish.

$$t=\sqrt{21}+4$$

t=\frac{8±2\sqrt{21}}{2} tenglamasini yeching, bunda ± manfiy. 8 dan 2\sqrt{21} ni ayirish.

$$t=\frac{8-2\sqrt{21}}{2}$$

8-2\sqrt{21} ni 2 ga bo'lish.

$$t=4-\sqrt{21}$$

Tenglama yechildi.

$$t=\sqrt{21}+4 t=4-\sqrt{21}$$

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.

$$t^{2}-8t-5=0$$

5 ni tenglamaning ikkala tarafiga qo'shish.

$$t^{2}-8t-5-\left(-5\right)=-\left(-5\right)$$

O‘zidan -5 ayirilsa 0 qoladi.

$$t^{2}-8t=-\left(-5\right)$$

0 dan -5 ni ayirish.

$$t^{2}-8t=5$$

-8 ni bo‘lish, x shartining koeffitsienti, 2 ga -4 olish uchun. Keyin, -4 ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$t^{2}-8t+\left(-4\right)^{2}=5+\left(-4\right)^{2}$$

-4 kvadratini chiqarish.

$$t^{2}-8t+16=5+16$$

5 ni 16 ga qo'shish.

$$t^{2}-8t+16=21$$

t^{2}-8t+16 omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(t-4\right)^{2}=21$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(t-4\right)^{2}}=\sqrt{21}$$

Qisqartirish.

$$t-4=\sqrt{21} t-4=-\sqrt{21}$$

4 ni tenglamaning ikkala tarafiga qo'shish.

$$t=\sqrt{21}+4 t=4-\sqrt{21}$$