-k+3/4-k=k-3 eching

$$\frac { - k + 3 } { 4 - k } = k - 3$$

k uchun yechish

$$k=3$$

$$k=5$$

Kvadrat tenglamalaridan foydalanish qoidalari

k qiymati 4 teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. Tenglamaning ikkala tarafini -k+4 ga ko'paytirish.

$$-k+3=\left(-k+4\right)k+\left(-k+4\right)\left(-3\right)$$

-k+4 ga k ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$-k+3=-k^{2}+4k+\left(-k+4\right)\left(-3\right)$$

-k+4 ga -3 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$-k+3=-k^{2}+4k+3k-12$$

7k ni olish uchun 4k va 3k ni birlashtirish.

$$-k+3=-k^{2}+7k-12$$

k^{2} ni ikki tarafga qo’shing.

$$-k+3+k^{2}=7k-12$$

Ikkala tarafdan 7k ni ayirish.

$$-k+3+k^{2}-7k=-12$$

12 ni ikki tarafga qo’shing.

$$-k+3+k^{2}-7k+12=0$$

15 olish uchun 3 va 12'ni qo'shing.

$$-k+15+k^{2}-7k=0$$

-8k ni olish uchun -k va -7k ni birlashtirish.

$$-8k+15+k^{2}=0$$

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.

$$k^{2}-8k+15=0$$

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 15 ni c bilan almashtiring.

$$k=\frac{-\left(-8\right)±\sqrt{\left(-8\right)^{2}-4\times 15}}{2}$$

-8 kvadratini chiqarish.

$$k=\frac{-\left(-8\right)±\sqrt{64-4\times 15}}{2}$$

-4 ni 15 marotabaga ko'paytirish.

$$k=\frac{-\left(-8\right)±\sqrt{64-60}}{2}$$

64 ni -60 ga qo'shish.

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

4 ning kvadrat ildizini chiqarish.

$$k=\frac{-\left(-8\right)±2}{2}$$

-8 ning teskarisi 8 ga teng.

$$k=\frac{8±2}{2}$$

k=\frac{8±2}{2} tenglamasini yeching, bunda ± musbat. 8 ni 2 ga qo'shish.

$$k=\frac{10}{2}$$

10 ni 2 ga bo'lish.

$$k=5$$

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

$$k=\frac{6}{2}$$

6 ni 2 ga bo'lish.

$$k=3$$

Tenglama yechildi.

$$k=5 k=3$$

Kvadratni yakunlash bo'yicha qadamlar

k qiymati 4 teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. Tenglamaning ikkala tarafini -k+4 ga ko'paytirish.

$$-k+3=\left(-k+4\right)k+\left(-k+4\right)\left(-3\right)$$

-k+4 ga k ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$-k+3=-k^{2}+4k+\left(-k+4\right)\left(-3\right)$$

-k+4 ga -3 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$-k+3=-k^{2}+4k+3k-12$$

7k ni olish uchun 4k va 3k ni birlashtirish.

$$-k+3=-k^{2}+7k-12$$

k^{2} ni ikki tarafga qo’shing.

$$-k+3+k^{2}=7k-12$$

Ikkala tarafdan 7k ni ayirish.

$$-k+3+k^{2}-7k=-12$$

Ikkala tarafdan 3 ni ayirish.

$$-k+k^{2}-7k=-12-3$$

-15 olish uchun -12 dan 3 ni ayirish.

$$-k+k^{2}-7k=-15$$

-8k ni olish uchun -k va -7k ni birlashtirish.

$$-8k+k^{2}=-15$$

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

$$k^{2}-8k=-15$$

-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.

$$k^{2}-8k+\left(-4\right)^{2}=-15+\left(-4\right)^{2}$$

-4 kvadratini chiqarish.

$$k^{2}-8k+16=-15+16$$

-15 ni 16 ga qo'shish.

$$k^{2}-8k+16=1$$

k^{2}-8k+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.

$$\left(k-4\right)^{2}=1$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(k-4\right)^{2}}=\sqrt{1}$$

Qisqartirish.

$$k-4=1 k-4=-1$$

4 ni tenglamaning ikkala tarafiga qo'shish.

$$k=5 k=3$$