a+2-4/2-a=59 eching

$$a + 2 - \frac { 4 } { 2 - a } = 59$$

a uchun yechish

$$a = \frac{\sqrt{3009} + 59}{2} \approx 56,927176304$$

$$a = \frac{59 - \sqrt{3009}}{2} \approx 2,072823696$$

Kvadrat tenglamalaridan foydalanish qoidalari

a qiymati 2 teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. Tenglamaning ikkala tarafini -a+2 ga ko'paytirish.

$$\left(-a+2\right)a+\left(-a+2\right)\times 2-4=59\left(-a+2\right)$$

-a+2 ga a ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$-a^{2}+2a+\left(-a+2\right)\times 2-4=59\left(-a+2\right)$$

-a+2 ga 2 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$-a^{2}+2a-2a+4-4=59\left(-a+2\right)$$

0 ni olish uchun 2a va -2a ni birlashtirish.

$$-a^{2}+4-4=59\left(-a+2\right)$$

0 olish uchun 4 dan 4 ni ayirish.

$$-a^{2}=59\left(-a+2\right)$$

59 ga -a+2 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$-a^{2}=-59a+118$$

59a ni ikki tarafga qo’shing.

$$-a^{2}+59a=118$$

Ikkala tarafdan 118 ni ayirish.

$$-a^{2}+59a-118=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} -1 ni a, 59 ni b va -118 ni c bilan almashtiring.

$$a=\frac{-59±\sqrt{59^{2}-4\left(-1\right)\left(-118\right)}}{2\left(-1\right)}$$

59 kvadratini chiqarish.

$$a=\frac{-59±\sqrt{3481-4\left(-1\right)\left(-118\right)}}{2\left(-1\right)}$$

-4 ni -1 marotabaga ko'paytirish.

$$a=\frac{-59±\sqrt{3481+4\left(-118\right)}}{2\left(-1\right)}$$

4 ni -118 marotabaga ko'paytirish.

$$a=\frac{-59±\sqrt{3481-472}}{2\left(-1\right)}$$

3481 ni -472 ga qo'shish.

$$a=\frac{-59±\sqrt{3009}}{2\left(-1\right)}$$

2 ni -1 marotabaga ko'paytirish.

$$a=\frac{-59±\sqrt{3009}}{-2}$$

a=\frac{-59±\sqrt{3009}}{-2} tenglamasini yeching, bunda ± musbat. -59 ni \sqrt{3009} ga qo'shish.

$$a=\frac{\sqrt{3009}-59}{-2}$$

-59+\sqrt{3009} ni -2 ga bo'lish.

$$a=\frac{59-\sqrt{3009}}{2}$$

a=\frac{-59±\sqrt{3009}}{-2} tenglamasini yeching, bunda ± manfiy. -59 dan \sqrt{3009} ni ayirish.

$$a=\frac{-\sqrt{3009}-59}{-2}$$

-59-\sqrt{3009} ni -2 ga bo'lish.

$$a=\frac{\sqrt{3009}+59}{2}$$

Tenglama yechildi.

$$a=\frac{59-\sqrt{3009}}{2} a=\frac{\sqrt{3009}+59}{2}$$

Kvadratni yakunlash bo'yicha qadamlar

a qiymati 2 teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. Tenglamaning ikkala tarafini -a+2 ga ko'paytirish.

$$\left(-a+2\right)a+\left(-a+2\right)\times 2-4=59\left(-a+2\right)$$

-a+2 ga a ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$-a^{2}+2a+\left(-a+2\right)\times 2-4=59\left(-a+2\right)$$

-a+2 ga 2 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$-a^{2}+2a-2a+4-4=59\left(-a+2\right)$$

0 ni olish uchun 2a va -2a ni birlashtirish.

$$-a^{2}+4-4=59\left(-a+2\right)$$

0 olish uchun 4 dan 4 ni ayirish.

$$-a^{2}=59\left(-a+2\right)$$

59 ga -a+2 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$-a^{2}=-59a+118$$

59a ni ikki tarafga qo’shing.

$$-a^{2}+59a=118$$

Ikki tarafini -1 ga bo‘ling.

$$\frac{-a^{2}+59a}{-1}=\frac{118}{-1}$$

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

$$a^{2}+\frac{59}{-1}a=\frac{118}{-1}$$

59 ni -1 ga bo'lish.

$$a^{2}-59a=\frac{118}{-1}$$

118 ni -1 ga bo'lish.

$$a^{2}-59a=-118$$

-59 ni bo‘lish, x shartining koeffitsienti, 2 ga -\frac{59}{2} olish uchun. Keyin, -\frac{59}{2} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$a^{2}-59a+\left(-\frac{59}{2}\right)^{2}=-118+\left(-\frac{59}{2}\right)^{2}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib -\frac{59}{2} kvadratini chiqarish.

$$a^{2}-59a+\frac{3481}{4}=-118+\frac{3481}{4}$$

-118 ni \frac{3481}{4} ga qo'shish.

$$a^{2}-59a+\frac{3481}{4}=\frac{3009}{4}$$

a^{2}-59a+\frac{3481}{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.

$$\left(a-\frac{59}{2}\right)^{2}=\frac{3009}{4}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(a-\frac{59}{2}\right)^{2}}=\sqrt{\frac{3009}{4}}$$

Qisqartirish.

$$a-\frac{59}{2}=\frac{\sqrt{3009}}{2} a-\frac{59}{2}=-\frac{\sqrt{3009}}{2}$$

\frac{59}{2} ni tenglamaning ikkala tarafiga qo'shish.

$$a=\frac{\sqrt{3009}+59}{2} a=\frac{59-\sqrt{3009}}{2}$$