48/x+4+48/x-4=5 eching

$$\frac { 48 } { x + 4 } + \frac { 48 } { x - 4 } = 5$$

x uchun yechish

$$x=20$$

$$x=-\frac{4}{5}=-0,8$$

Kvadrat tenglamalaridan foydalanish qoidalari

x qiymati -4,4 qiymatlaridan birortasiga teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. Tenglamaning ikkala tarafini \left(x-4\right)\left(x+4\right) ga, x+4,x-4 ning eng kichik karralisiga ko‘paytiring.

$$\left(x-4\right)\times 48+\left(x+4\right)\times 48=5\left(x-4\right)\left(x+4\right)$$

x-4 ga 48 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$48x-192+\left(x+4\right)\times 48=5\left(x-4\right)\left(x+4\right)$$

x+4 ga 48 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$48x-192+48x+192=5\left(x-4\right)\left(x+4\right)$$

96x ni olish uchun 48x va 48x ni birlashtirish.

$$96x-192+192=5\left(x-4\right)\left(x+4\right)$$

0 olish uchun -192 va 192'ni qo'shing.

$$96x=5\left(x-4\right)\left(x+4\right)$$

5 ga x-4 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$96x=\left(5x-20\right)\left(x+4\right)$$

5x-20 ga x+4 ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

$$96x=5x^{2}-80$$

Ikkala tarafdan 5x^{2} ni ayirish.

$$96x-5x^{2}=-80$$

80 ni ikki tarafga qo’shing.

$$96x-5x^{2}+80=0$$

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.

$$-5x^{2}+96x+80=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} -5 ni a, 96 ni b va 80 ni c bilan almashtiring.

$$x=\frac{-96±\sqrt{96^{2}-4\left(-5\right)\times 80}}{2\left(-5\right)}$$

96 kvadratini chiqarish.

$$x=\frac{-96±\sqrt{9216-4\left(-5\right)\times 80}}{2\left(-5\right)}$$

-4 ni -5 marotabaga ko'paytirish.

$$x=\frac{-96±\sqrt{9216+20\times 80}}{2\left(-5\right)}$$

20 ni 80 marotabaga ko'paytirish.

$$x=\frac{-96±\sqrt{9216+1600}}{2\left(-5\right)}$$

9216 ni 1600 ga qo'shish.

$$x=\frac{-96±\sqrt{10816}}{2\left(-5\right)}$$

10816 ning kvadrat ildizini chiqarish.

$$x=\frac{-96±104}{2\left(-5\right)}$$

2 ni -5 marotabaga ko'paytirish.

$$x=\frac{-96±104}{-10}$$

x=\frac{-96±104}{-10} tenglamasini yeching, bunda ± musbat. -96 ni 104 ga qo'shish.

$$x=\frac{8}{-10}$$

\frac{8}{-10} ulushini 2 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$x=-\frac{4}{5}$$

x=\frac{-96±104}{-10} tenglamasini yeching, bunda ± manfiy. -96 dan 104 ni ayirish.

$$x=-\frac{200}{-10}$$

-200 ni -10 ga bo'lish.

$$x=20$$

Tenglama yechildi.

$$x=-\frac{4}{5} x=20$$

Kvadratni yakunlash bo'yicha qadamlar

x qiymati -4,4 qiymatlaridan birortasiga teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. Tenglamaning ikkala tarafini \left(x-4\right)\left(x+4\right) ga, x+4,x-4 ning eng kichik karralisiga ko‘paytiring.

$$\left(x-4\right)\times 48+\left(x+4\right)\times 48=5\left(x-4\right)\left(x+4\right)$$

x-4 ga 48 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$48x-192+\left(x+4\right)\times 48=5\left(x-4\right)\left(x+4\right)$$

x+4 ga 48 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$48x-192+48x+192=5\left(x-4\right)\left(x+4\right)$$

96x ni olish uchun 48x va 48x ni birlashtirish.

$$96x-192+192=5\left(x-4\right)\left(x+4\right)$$

0 olish uchun -192 va 192'ni qo'shing.

$$96x=5\left(x-4\right)\left(x+4\right)$$

5 ga x-4 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$96x=\left(5x-20\right)\left(x+4\right)$$

5x-20 ga x+4 ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

$$96x=5x^{2}-80$$

Ikkala tarafdan 5x^{2} ni ayirish.

$$96x-5x^{2}=-80$$

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

$$-5x^{2}+96x=-80$$

Ikki tarafini -5 ga bo‘ling.

$$\frac{-5x^{2}+96x}{-5}=-\frac{80}{-5}$$

-5 ga bo'lish -5 ga ko'paytirishni bekor qiladi.

$$x^{2}+\frac{96}{-5}x=-\frac{80}{-5}$$

96 ni -5 ga bo'lish.

$$x^{2}-\frac{96}{5}x=-\frac{80}{-5}$$

-80 ni -5 ga bo'lish.

$$x^{2}-\frac{96}{5}x=16$$

-\frac{96}{5} ni bo‘lish, x shartining koeffitsienti, 2 ga -\frac{48}{5} olish uchun. Keyin, -\frac{48}{5} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}-\frac{96}{5}x+\left(-\frac{48}{5}\right)^{2}=16+\left(-\frac{48}{5}\right)^{2}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib -\frac{48}{5} kvadratini chiqarish.

$$x^{2}-\frac{96}{5}x+\frac{2304}{25}=16+\frac{2304}{25}$$

16 ni \frac{2304}{25} ga qo'shish.

$$x^{2}-\frac{96}{5}x+\frac{2304}{25}=\frac{2704}{25}$$

x^{2}-\frac{96}{5}x+\frac{2304}{25} omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x-\frac{48}{5}\right)^{2}=\frac{2704}{25}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-\frac{48}{5}\right)^{2}}=\sqrt{\frac{2704}{25}}$$

Qisqartirish.

$$x-\frac{48}{5}=\frac{52}{5} x-\frac{48}{5}=-\frac{52}{5}$$

\frac{48}{5} ni tenglamaning ikkala tarafiga qo'shish.

$$x=20 x=-\frac{4}{5}$$