AA+2A=65 eching

$$A A + 2 A = 65$$

A uchun yechish (complex solution)

$$A=\sqrt{66}-1\approx 7,124038405$$

$$A=-\left(\sqrt{66}+1\right)\approx -9,124038405$$

Kvadrat tenglamalaridan foydalanish qoidalari

A^{2} hosil qilish uchun A va A ni ko'paytirish.

$$A^{2}+2A=65$$

Ikkala tarafdan 65 ni ayirish.

$$A^{2}+2A-65=0$$

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 -65 ni c bilan almashtiring.

$$A=\frac{-2±\sqrt{2^{2}-4\left(-65\right)}}{2}$$

2 kvadratini chiqarish.

$$A=\frac{-2±\sqrt{4-4\left(-65\right)}}{2}$$

-4 ni -65 marotabaga ko'paytirish.

$$A=\frac{-2±\sqrt{4+260}}{2}$$

4 ni 260 ga qo'shish.

$$A=\frac{-2±\sqrt{264}}{2}$$

264 ning kvadrat ildizini chiqarish.

$$A=\frac{-2±2\sqrt{66}}{2}$$

A=\frac{-2±2\sqrt{66}}{2} tenglamasini yeching, bunda ± musbat. -2 ni 2\sqrt{66} ga qo'shish.

$$A=\frac{2\sqrt{66}-2}{2}$$

-2+2\sqrt{66} ni 2 ga bo'lish.

$$A=\sqrt{66}-1$$

A=\frac{-2±2\sqrt{66}}{2} tenglamasini yeching, bunda ± manfiy. -2 dan 2\sqrt{66} ni ayirish.

$$A=\frac{-2\sqrt{66}-2}{2}$$

-2-2\sqrt{66} ni 2 ga bo'lish.

$$A=-\sqrt{66}-1$$

Tenglama yechildi.

$$A=\sqrt{66}-1 A=-\sqrt{66}-1$$

Kvadratni yakunlash bo'yicha qadamlar

A^{2} hosil qilish uchun A va A ni ko'paytirish.

$$A^{2}+2A=65$$

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.

$$A^{2}+2A+1^{2}=65+1^{2}$$

1 kvadratini chiqarish.

$$A^{2}+2A+1=65+1$$

65 ni 1 ga qo'shish.

$$A^{2}+2A+1=66$$

A^{2}+2A+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.

$$\left(A+1\right)^{2}=66$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(A+1\right)^{2}}=\sqrt{66}$$

Qisqartirish.

$$A+1=\sqrt{66} A+1=-\sqrt{66}$$

Tenglamaning ikkala tarafidan 1 ni ayirish.

$$A=\sqrt{66}-1 A=-\sqrt{66}-1$$

A uchun yechish

$$A=\sqrt{66}-1\approx 7,124038405$$

$$A=-\sqrt{66}-1\approx -9,124038405$$

Kvadrat tenglamalaridan foydalanish qoidalari

A^{2} hosil qilish uchun A va A ni ko'paytirish.

$$A^{2}+2A=65$$

Ikkala tarafdan 65 ni ayirish.

$$A^{2}+2A-65=0$$

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 -65 ni c bilan almashtiring.

$$A=\frac{-2±\sqrt{2^{2}-4\left(-65\right)}}{2}$$

2 kvadratini chiqarish.

$$A=\frac{-2±\sqrt{4-4\left(-65\right)}}{2}$$

-4 ni -65 marotabaga ko'paytirish.

$$A=\frac{-2±\sqrt{4+260}}{2}$$

4 ni 260 ga qo'shish.

$$A=\frac{-2±\sqrt{264}}{2}$$

264 ning kvadrat ildizini chiqarish.

$$A=\frac{-2±2\sqrt{66}}{2}$$

A=\frac{-2±2\sqrt{66}}{2} tenglamasini yeching, bunda ± musbat. -2 ni 2\sqrt{66} ga qo'shish.

$$A=\frac{2\sqrt{66}-2}{2}$$

-2+2\sqrt{66} ni 2 ga bo'lish.

$$A=\sqrt{66}-1$$

A=\frac{-2±2\sqrt{66}}{2} tenglamasini yeching, bunda ± manfiy. -2 dan 2\sqrt{66} ni ayirish.

$$A=\frac{-2\sqrt{66}-2}{2}$$

-2-2\sqrt{66} ni 2 ga bo'lish.

$$A=-\sqrt{66}-1$$

Tenglama yechildi.

$$A=\sqrt{66}-1 A=-\sqrt{66}-1$$

Kvadratni yakunlash bo'yicha qadamlar

A^{2} hosil qilish uchun A va A ni ko'paytirish.

$$A^{2}+2A=65$$

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.

$$A^{2}+2A+1^{2}=65+1^{2}$$

1 kvadratini chiqarish.

$$A^{2}+2A+1=65+1$$

65 ni 1 ga qo'shish.

$$A^{2}+2A+1=66$$

A^{2}+2A+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.

$$\left(A+1\right)^{2}=66$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(A+1\right)^{2}}=\sqrt{66}$$

Qisqartirish.

$$A+1=\sqrt{66} A+1=-\sqrt{66}$$

Tenglamaning ikkala tarafidan 1 ni ayirish.

$$A=\sqrt{66}-1 A=-\sqrt{66}-1$$