frac{x^{2}+7^2-4^2}{14x}=7^2+4x^2-36/14x eching

$$\frac { x ^ { 2 } + 7 ^ { 2 } - 4 ^ { 2 } } { 14 x } = \frac { 7 ^ { 2 } + 4 x ^ { 2 } - 36 } { 14 x }$$

x uchun yechish

$$x = \frac{2 \sqrt{15}}{3} \approx 2,581988897$$

$$x = -\frac{2 \sqrt{15}}{3} \approx -2,581988897$$

Kvadrat ildizini topish bo'yicha qadamlar

x qiymati 0 teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. Tenglamaning ikkala tarafini 14x ga ko'paytirish.

$$x^{2}+7^{2}-4^{2}=7^{2}+4x^{2}-36$$

2 daraja ko‘rsatkichini 7 ga hisoblang va 49 ni qiymatni oling.

$$x^{2}+49-4^{2}=7^{2}+4x^{2}-36$$

2 daraja ko‘rsatkichini 4 ga hisoblang va 16 ni qiymatni oling.

$$x^{2}+49-16=7^{2}+4x^{2}-36$$

33 olish uchun 49 dan 16 ni ayirish.

$$x^{2}+33=7^{2}+4x^{2}-36$$

2 daraja ko‘rsatkichini 7 ga hisoblang va 49 ni qiymatni oling.

$$x^{2}+33=49+4x^{2}-36$$

13 olish uchun 49 dan 36 ni ayirish.

$$x^{2}+33=13+4x^{2}$$

Ikkala tarafdan 4x^{2} ni ayirish.

$$x^{2}+33-4x^{2}=13$$

-3x^{2} ni olish uchun x^{2} va -4x^{2} ni birlashtirish.

$$-3x^{2}+33=13$$

Ikkala tarafdan 33 ni ayirish.

$$-3x^{2}=13-33$$

-20 olish uchun 13 dan 33 ni ayirish.

$$-3x^{2}=-20$$

Ikki tarafini -3 ga bo‘ling.

$$x^{2}=\frac{-20}{-3}$$

Ikkala surat va maxrajdan manfiy belgini olib tashlash bilan \frac{-20}{-3} kasrini \frac{20}{3} ga soddalashtirish mumkin.

$$x^{2}=\frac{20}{3}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$x=\frac{2\sqrt{15}}{3} x=-\frac{2\sqrt{15}}{3}$$

Kvadrat tenglamalaridan foydalanish qoidalari

x qiymati 0 teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. Tenglamaning ikkala tarafini 14x ga ko'paytirish.

$$x^{2}+7^{2}-4^{2}=7^{2}+4x^{2}-36$$

2 daraja ko‘rsatkichini 7 ga hisoblang va 49 ni qiymatni oling.

$$x^{2}+49-4^{2}=7^{2}+4x^{2}-36$$

2 daraja ko‘rsatkichini 4 ga hisoblang va 16 ni qiymatni oling.

$$x^{2}+49-16=7^{2}+4x^{2}-36$$

33 olish uchun 49 dan 16 ni ayirish.

$$x^{2}+33=7^{2}+4x^{2}-36$$

2 daraja ko‘rsatkichini 7 ga hisoblang va 49 ni qiymatni oling.

$$x^{2}+33=49+4x^{2}-36$$

13 olish uchun 49 dan 36 ni ayirish.

$$x^{2}+33=13+4x^{2}$$

Ikkala tarafdan 13 ni ayirish.

$$x^{2}+33-13=4x^{2}$$

20 olish uchun 33 dan 13 ni ayirish.

$$x^{2}+20=4x^{2}$$

Ikkala tarafdan 4x^{2} ni ayirish.

$$x^{2}+20-4x^{2}=0$$

-3x^{2} ni olish uchun x^{2} va -4x^{2} ni birlashtirish.

$$-3x^{2}+20=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} -3 ni a, 0 ni b va 20 ni c bilan almashtiring.

$$x=\frac{0±\sqrt{0^{2}-4\left(-3\right)\times 20}}{2\left(-3\right)}$$

0 kvadratini chiqarish.

$$x=\frac{0±\sqrt{-4\left(-3\right)\times 20}}{2\left(-3\right)}$$

-4 ni -3 marotabaga ko'paytirish.

$$x=\frac{0±\sqrt{12\times 20}}{2\left(-3\right)}$$

12 ni 20 marotabaga ko'paytirish.

$$x=\frac{0±\sqrt{240}}{2\left(-3\right)}$$

240 ning kvadrat ildizini chiqarish.

$$x=\frac{0±4\sqrt{15}}{2\left(-3\right)}$$

2 ni -3 marotabaga ko'paytirish.

$$x=\frac{0±4\sqrt{15}}{-6}$$

x=\frac{0±4\sqrt{15}}{-6} tenglamasini yeching, bunda ± musbat.

$$x=-\frac{2\sqrt{15}}{3}$$

x=\frac{0±4\sqrt{15}}{-6} tenglamasini yeching, bunda ± manfiy.

$$x=\frac{2\sqrt{15}}{3}$$

Tenglama yechildi.

$$x=-\frac{2\sqrt{15}}{3} x=\frac{2\sqrt{15}}{3}$$