(8/5+1/3):x=x:(1+14/15) eching

$$( \frac { 8 } { 5 } + \frac { 1 } { 3 } ) : x = x : ( 1 + \frac { 14 } { 15 } )$$

x uchun yechish

$$x = \frac{29}{15} = 1\frac{14}{15} \approx 1,933333333$$

$$x = -\frac{29}{15} = -1\frac{14}{15} \approx -1,933333333$$

Kvadrat ildizini topish bo'yicha qadamlar

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

$$\frac{8}{5}+\frac{1}{3}=\frac{15}{29}xx$$

5 va 3 ning eng kichik umumiy karralisi 15 ga teng. \frac{8}{5} va \frac{1}{3} ni 15 maxraj bilan kasrlarga aylantirib oling.

$$\frac{24}{15}+\frac{5}{15}=\frac{15}{29}xx$$

\frac{24}{15} va \frac{5}{15} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

$$\frac{24+5}{15}=\frac{15}{29}xx$$

29 olish uchun 24 va 5'ni qo'shing.

$$\frac{29}{15}=\frac{15}{29}xx$$

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

$$\frac{29}{15}=\frac{15}{29}x^{2}$$

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$\frac{15}{29}x^{2}=\frac{29}{15}$$

Ikki tarafini \frac{29}{15} va teskari kasri \frac{15}{29} ga ko‘paytiring.

$$x^{2}=\frac{29}{15}\times \frac{29}{15}$$

Suratni maxrajga va maxrajini suratga ko‘paytirish orqali \frac{29}{15} ni \frac{29}{15} ga ko‘paytiring.

$$x^{2}=\frac{29\times 29}{15\times 15}$$

\frac{29\times 29}{15\times 15} kasridagi ko‘paytirishlarni bajaring.

$$x^{2}=\frac{841}{225}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$x=\frac{29}{15} x=-\frac{29}{15}$$

Kvadrat tenglamalaridan foydalanish qoidalari

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

$$\frac{8}{5}+\frac{1}{3}=\frac{15}{29}xx$$

5 va 3 ning eng kichik umumiy karralisi 15 ga teng. \frac{8}{5} va \frac{1}{3} ni 15 maxraj bilan kasrlarga aylantirib oling.

$$\frac{24}{15}+\frac{5}{15}=\frac{15}{29}xx$$

\frac{24}{15} va \frac{5}{15} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

$$\frac{24+5}{15}=\frac{15}{29}xx$$

29 olish uchun 24 va 5'ni qo'shing.

$$\frac{29}{15}=\frac{15}{29}xx$$

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

$$\frac{29}{15}=\frac{15}{29}x^{2}$$

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$\frac{15}{29}x^{2}=\frac{29}{15}$$

Ikkala tarafdan \frac{29}{15} ni ayirish.

$$\frac{15}{29}x^{2}-\frac{29}{15}=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} \frac{15}{29} ni a, 0 ni b va -\frac{29}{15} ni c bilan almashtiring.

$$x=\frac{0±\sqrt{0^{2}-4\times \frac{15}{29}\left(-\frac{29}{15}\right)}}{2\times \frac{15}{29}}$$

0 kvadratini chiqarish.

$$x=\frac{0±\sqrt{-4\times \frac{15}{29}\left(-\frac{29}{15}\right)}}{2\times \frac{15}{29}}$$

-4 ni \frac{15}{29} marotabaga ko'paytirish.

$$x=\frac{0±\sqrt{-\frac{60}{29}\left(-\frac{29}{15}\right)}}{2\times \frac{15}{29}}$$

Raqamlash sonlarini va maxraj sonlariga ko'paytirish orqali -\frac{60}{29} ni -\frac{29}{15} ga ko'paytirish. So'ngra kasrni imkoni boricha eng kam a'zoga qisqartiring.

$$x=\frac{0±\sqrt{4}}{2\times \frac{15}{29}}$$

4 ning kvadrat ildizini chiqarish.

$$x=\frac{0±2}{2\times \frac{15}{29}}$$

2 ni \frac{15}{29} marotabaga ko'paytirish.

$$x=\frac{0±2}{\frac{30}{29}}$$

x=\frac{0±2}{\frac{30}{29}} tenglamasini yeching, bunda ± musbat. 2 ni \frac{30}{29} ga bo'lish 2 ga k'paytirish \frac{30}{29} ga qaytarish.

$$x=\frac{29}{15}$$

x=\frac{0±2}{\frac{30}{29}} tenglamasini yeching, bunda ± manfiy. -2 ni \frac{30}{29} ga bo'lish -2 ga k'paytirish \frac{30}{29} ga qaytarish.

$$x=-\frac{29}{15}$$

Tenglama yechildi.

$$x=\frac{29}{15} x=-\frac{29}{15}$$