-t^2+4t-280/t^2-4t=0 eching

$$\frac{ - { t }^{ 2 } +4t-280 }{ { t }^{ 2 } -4t } = 0$$

t uchun yechish

$$t=-2\sqrt{69}i+2\approx 2-16,613247726i$$

$$t=2+2\sqrt{69}i\approx 2+16,613247726i$$

Kvadrat tenglamalaridan foydalanish qoidalari

t qiymati 0,4 qiymatlaridan birortasiga teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. Tenglamaning ikkala tarafini t\left(t-4\right) ga ko'paytirish.

$$-t^{2}+4t-280=0$$

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 -280 ni c bilan almashtiring.

$$t=\frac{-4±\sqrt{4^{2}-4\left(-1\right)\left(-280\right)}}{2\left(-1\right)}$$

4 kvadratini chiqarish.

$$t=\frac{-4±\sqrt{16-4\left(-1\right)\left(-280\right)}}{2\left(-1\right)}$$

-4 ni -1 marotabaga ko'paytirish.

$$t=\frac{-4±\sqrt{16+4\left(-280\right)}}{2\left(-1\right)}$$

4 ni -280 marotabaga ko'paytirish.

$$t=\frac{-4±\sqrt{16-1120}}{2\left(-1\right)}$$

16 ni -1120 ga qo'shish.

$$t=\frac{-4±\sqrt{-1104}}{2\left(-1\right)}$$

-1104 ning kvadrat ildizini chiqarish.

$$t=\frac{-4±4\sqrt{69}i}{2\left(-1\right)}$$

2 ni -1 marotabaga ko'paytirish.

$$t=\frac{-4±4\sqrt{69}i}{-2}$$

t=\frac{-4±4\sqrt{69}i}{-2} tenglamasini yeching, bunda ± musbat. -4 ni 4i\sqrt{69} ga qo'shish.

$$t=\frac{-4+4\sqrt{69}i}{-2}$$

-4+4i\sqrt{69} ni -2 ga bo'lish.

$$t=-2\sqrt{69}i+2$$

t=\frac{-4±4\sqrt{69}i}{-2} tenglamasini yeching, bunda ± manfiy. -4 dan 4i\sqrt{69} ni ayirish.

$$t=\frac{-4\sqrt{69}i-4}{-2}$$

-4-4i\sqrt{69} ni -2 ga bo'lish.

$$t=2+2\sqrt{69}i$$

Tenglama yechildi.

$$t=-2\sqrt{69}i+2 t=2+2\sqrt{69}i$$

Kvadratni yakunlash bo'yicha qadamlar

t qiymati 0,4 qiymatlaridan birortasiga teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. Tenglamaning ikkala tarafini t\left(t-4\right) ga ko'paytirish.

$$-t^{2}+4t-280=0$$

280 ni ikki tarafga qo’shing. Har qanday songa nolni qo‘shsangiz, o‘zi chiqadi.

$$-t^{2}+4t=280$$

Ikki tarafini -1 ga bo‘ling.

$$\frac{-t^{2}+4t}{-1}=\frac{280}{-1}$$

-1 ga bo'lish -1 ga ko'paytirishni bekor qiladi.

$$t^{2}+\frac{4}{-1}t=\frac{280}{-1}$$

4 ni -1 ga bo'lish.

$$t^{2}-4t=\frac{280}{-1}$$

280 ni -1 ga bo'lish.

$$t^{2}-4t=-280$$

-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.

$$t^{2}-4t+\left(-2\right)^{2}=-280+\left(-2\right)^{2}$$

-2 kvadratini chiqarish.

$$t^{2}-4t+4=-280+4$$

-280 ni 4 ga qo'shish.

$$t^{2}-4t+4=-276$$

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.

$$\left(t-2\right)^{2}=-276$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(t-2\right)^{2}}=\sqrt{-276}$$

Qisqartirish.

$$t-2=2\sqrt{69}i t-2=-2\sqrt{69}i$$

2 ni tenglamaning ikkala tarafiga qo'shish.

$$t=2+2\sqrt{69}i t=-2\sqrt{69}i+2$$