3x-4/7+7/3x-4=5/2.xneq4/3 eching

$$\frac { 3 x - 4 } { 7 } + \frac { 7 } { 3 x - 4 } = \frac { 5 } { 2 } . x \neq \frac { 4 } { 3 }$$

x uchun yechish

$$x=6$$

$$x = \frac{5}{2} = 2\frac{1}{2} = 2,5$$

Kvadrat tenglamalaridan foydalanish qoidalari

x qiymati \frac{4}{3} teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. Tenglamaning ikkala tarafini 14\left(3x-4\right) ga, 7,3x-4,2 ning eng kichik karralisiga ko‘paytiring.

$$\left(6x-8\right)\left(3x-4\right)+14\times 7=35\left(3x-4\right)$$

6x-8 ga 3x-4 ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

$$18x^{2}-48x+32+14\times 7=35\left(3x-4\right)$$

98 hosil qilish uchun 14 va 7 ni ko'paytirish.

$$18x^{2}-48x+32+98=35\left(3x-4\right)$$

130 olish uchun 32 va 98'ni qo'shing.

$$18x^{2}-48x+130=35\left(3x-4\right)$$

35 ga 3x-4 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$18x^{2}-48x+130=105x-140$$

Ikkala tarafdan 105x ni ayirish.

$$18x^{2}-48x+130-105x=-140$$

-153x ni olish uchun -48x va -105x ni birlashtirish.

$$18x^{2}-153x+130=-140$$

140 ni ikki tarafga qo’shing.

$$18x^{2}-153x+130+140=0$$

270 olish uchun 130 va 140'ni qo'shing.

$$18x^{2}-153x+270=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 18 ni a, -153 ni b va 270 ni c bilan almashtiring.

$$x=\frac{-\left(-153\right)±\sqrt{\left(-153\right)^{2}-4\times 18\times 270}}{2\times 18}$$

-153 kvadratini chiqarish.

$$x=\frac{-\left(-153\right)±\sqrt{23409-4\times 18\times 270}}{2\times 18}$$

-4 ni 18 marotabaga ko'paytirish.

$$x=\frac{-\left(-153\right)±\sqrt{23409-72\times 270}}{2\times 18}$$

-72 ni 270 marotabaga ko'paytirish.

$$x=\frac{-\left(-153\right)±\sqrt{23409-19440}}{2\times 18}$$

23409 ni -19440 ga qo'shish.

$$x=\frac{-\left(-153\right)±\sqrt{3969}}{2\times 18}$$

3969 ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-153\right)±63}{2\times 18}$$

-153 ning teskarisi 153 ga teng.

$$x=\frac{153±63}{2\times 18}$$

2 ni 18 marotabaga ko'paytirish.

$$x=\frac{153±63}{36}$$

x=\frac{153±63}{36} tenglamasini yeching, bunda ± musbat. 153 ni 63 ga qo'shish.

$$x=\frac{216}{36}$$

216 ni 36 ga bo'lish.

$$x=6$$

x=\frac{153±63}{36} tenglamasini yeching, bunda ± manfiy. 153 dan 63 ni ayirish.

$$x=\frac{90}{36}$$

\frac{90}{36} ulushini 18 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$x=\frac{5}{2}$$

Tenglama yechildi.

$$x=6 x=\frac{5}{2}$$

Kvadratni yakunlash bo'yicha qadamlar

x qiymati \frac{4}{3} teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. Tenglamaning ikkala tarafini 14\left(3x-4\right) ga, 7,3x-4,2 ning eng kichik karralisiga ko‘paytiring.

$$\left(6x-8\right)\left(3x-4\right)+14\times 7=35\left(3x-4\right)$$

6x-8 ga 3x-4 ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

$$18x^{2}-48x+32+14\times 7=35\left(3x-4\right)$$

98 hosil qilish uchun 14 va 7 ni ko'paytirish.

$$18x^{2}-48x+32+98=35\left(3x-4\right)$$

130 olish uchun 32 va 98'ni qo'shing.

$$18x^{2}-48x+130=35\left(3x-4\right)$$

35 ga 3x-4 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$18x^{2}-48x+130=105x-140$$

Ikkala tarafdan 105x ni ayirish.

$$18x^{2}-48x+130-105x=-140$$

-153x ni olish uchun -48x va -105x ni birlashtirish.

$$18x^{2}-153x+130=-140$$

Ikkala tarafdan 130 ni ayirish.

$$18x^{2}-153x=-140-130$$

-270 olish uchun -140 dan 130 ni ayirish.

$$18x^{2}-153x=-270$$

Ikki tarafini 18 ga bo‘ling.

$$\frac{18x^{2}-153x}{18}=-\frac{270}{18}$$

18 ga bo'lish 18 ga ko'paytirishni bekor qiladi.

$$x^{2}+\left(-\frac{153}{18}\right)x=-\frac{270}{18}$$

\frac{-153}{18} ulushini 9 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$x^{2}-\frac{17}{2}x=-\frac{270}{18}$$

-270 ni 18 ga bo'lish.

$$x^{2}-\frac{17}{2}x=-15$$

-\frac{17}{2} ni bo‘lish, x shartining koeffitsienti, 2 ga -\frac{17}{4} olish uchun. Keyin, -\frac{17}{4} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}-\frac{17}{2}x+\left(-\frac{17}{4}\right)^{2}=-15+\left(-\frac{17}{4}\right)^{2}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib -\frac{17}{4} kvadratini chiqarish.

$$x^{2}-\frac{17}{2}x+\frac{289}{16}=-15+\frac{289}{16}$$

-15 ni \frac{289}{16} ga qo'shish.

$$x^{2}-\frac{17}{2}x+\frac{289}{16}=\frac{49}{16}$$

x^{2}-\frac{17}{2}x+\frac{289}{16} omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x-\frac{17}{4}\right)^{2}=\frac{49}{16}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-\frac{17}{4}\right)^{2}}=\sqrt{\frac{49}{16}}$$

Qisqartirish.

$$x-\frac{17}{4}=\frac{7}{4} x-\frac{17}{4}=-\frac{7}{4}$$

\frac{17}{4} ni tenglamaning ikkala tarafiga qo'shish.

$$x=6 x=\frac{5}{2}$$