n^2+2n-1=6 eching

$$n ^ { 2 } + 2 n - 1 = 6$$

n uchun yechish

$$n=2\sqrt{2}-1\approx 1,828427125$$

$$n=-2\sqrt{2}-1\approx -3,828427125$$

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.

$$n^{2}+2n-1=6$$

Tenglamaning ikkala tarafidan 6 ni ayirish.

$$n^{2}+2n-1-6=6-6$$

O‘zidan 6 ayirilsa 0 qoladi.

$$n^{2}+2n-1-6=0$$

-1 dan 6 ni ayirish.

$$n^{2}+2n-7=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 1 ni a, 2 ni b va -7 ni c bilan almashtiring.

$$n=\frac{-2±\sqrt{2^{2}-4\left(-7\right)}}{2}$$

2 kvadratini chiqarish.

$$n=\frac{-2±\sqrt{4-4\left(-7\right)}}{2}$$

-4 ni -7 marotabaga ko'paytirish.

$$n=\frac{-2±\sqrt{4+28}}{2}$$

4 ni 28 ga qo'shish.

$$n=\frac{-2±\sqrt{32}}{2}$$

32 ning kvadrat ildizini chiqarish.

$$n=\frac{-2±4\sqrt{2}}{2}$$

n=\frac{-2±4\sqrt{2}}{2} tenglamasini yeching, bunda ± musbat. -2 ni 4\sqrt{2} ga qo'shish.

$$n=\frac{4\sqrt{2}-2}{2}$$

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

$$n=2\sqrt{2}-1$$

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

$$n=\frac{-4\sqrt{2}-2}{2}$$

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

$$n=-2\sqrt{2}-1$$

Tenglama yechildi.

$$n=2\sqrt{2}-1 n=-2\sqrt{2}-1$$

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.

$$n^{2}+2n-1=6$$

1 ni tenglamaning ikkala tarafiga qo'shish.

$$n^{2}+2n-1-\left(-1\right)=6-\left(-1\right)$$

O‘zidan -1 ayirilsa 0 qoladi.

$$n^{2}+2n=6-\left(-1\right)$$

6 dan -1 ni ayirish.

$$n^{2}+2n=7$$

2 ni bo‘lish, x shartining koeffitsienti, 2 ga 1 olish uchun. Keyin, 1 ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$n^{2}+2n+1^{2}=7+1^{2}$$

1 kvadratini chiqarish.

$$n^{2}+2n+1=7+1$$

7 ni 1 ga qo'shish.

$$n^{2}+2n+1=8$$

n^{2}+2n+1 omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(n+1\right)^{2}=8$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(n+1\right)^{2}}=\sqrt{8}$$

Qisqartirish.

$$n+1=2\sqrt{2} n+1=-2\sqrt{2}$$

Tenglamaning ikkala tarafidan 1 ni ayirish.

$$n=2\sqrt{2}-1 n=-2\sqrt{2}-1$$