(1/5x+1)(1-1/5x)+(x/5-5/3)^2=0 eching

$$( \frac { 1 } { 5 } x + 1 ) ( 1 - \frac { 1 } { 5 } x ) + ( \frac { x } { 5 } - \frac { 5 } { 3 } ) ^ { 2 } = 0$$

x uchun yechish

$$x = \frac{17}{3} = 5\frac{2}{3} \approx 5,666666667$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

Hisoblang: \left(\frac{1}{5}x+1\right)\left(1-\frac{1}{5}x\right). Ko‘paytirish qoida yordamida turli kvadratlarga aylantirilishi mumkin: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}. 1 kvadratini chiqarish.

$$1-\left(\frac{1}{5}x\right)^{2}+\left(\frac{x}{5}-\frac{5}{3}\right)^{2}=0$$

\left(\frac{1}{5}x\right)^{2} ni kengaytirish.

$$1-\left(\frac{1}{5}\right)^{2}x^{2}+\left(\frac{x}{5}-\frac{5}{3}\right)^{2}=0$$

2 daraja ko‘rsatkichini \frac{1}{5} ga hisoblang va \frac{1}{25} ni qiymatni oling.

$$1-\frac{1}{25}x^{2}+\left(\frac{x}{5}-\frac{5}{3}\right)^{2}=0$$

Ifodalarni qo‘shish yoki ayirish uchun ularni yoyib, maxrajlarini bir xil qiling. 5 va 3 ning eng kichik umumiy karralisi 15. \frac{x}{5} ni \frac{3}{3} marotabaga ko'paytirish. \frac{5}{3} ni \frac{5}{5} marotabaga ko'paytirish.

$$1-\frac{1}{25}x^{2}+\left(\frac{3x}{15}-\frac{5\times 5}{15}\right)^{2}=0$$

\frac{3x}{15} va \frac{5\times 5}{15} da bir xil maxraji bor, ularning suratini ayirish orqali ayiring.

$$1-\frac{1}{25}x^{2}+\left(\frac{3x-5\times 5}{15}\right)^{2}=0$$

3x-5\times 5 ichidagi ko‘paytirishlarni bajaring.

$$1-\frac{1}{25}x^{2}+\left(\frac{3x-25}{15}\right)^{2}=0$$

\frac{3x-25}{15}ni darajaga oshirish uchun, surat va maxrajni darajaga oshirib, keyin bo‘ling.

$$1-\frac{1}{25}x^{2}+\frac{\left(3x-25\right)^{2}}{15^{2}}=0$$

\left(a-b\right)^{2}=a^{2}-2ab+b^{2} binom teoremasini \left(3x-25\right)^{2} kengaytirilishi uchun ishlating.

$$1-\frac{1}{25}x^{2}+\frac{9x^{2}-150x+625}{15^{2}}=0$$

2 daraja ko‘rsatkichini 15 ga hisoblang va 225 ni qiymatni oling.

$$1-\frac{1}{25}x^{2}+\frac{9x^{2}-150x+625}{225}=0$$

\frac{1}{25}x^{2}-\frac{2}{3}x+\frac{25}{9} natijani olish uchun 9x^{2}-150x+625 ning har bir ifodasini 225 ga bo‘ling.

$$1-\frac{1}{25}x^{2}+\frac{1}{25}x^{2}-\frac{2}{3}x+\frac{25}{9}=0$$

0 ni olish uchun -\frac{1}{25}x^{2} va \frac{1}{25}x^{2} ni birlashtirish.

$$1-\frac{2}{3}x+\frac{25}{9}=0$$

\frac{34}{9} olish uchun 1 va \frac{25}{9}'ni qo'shing.

$$\frac{34}{9}-\frac{2}{3}x=0$$

Ikkala tarafdan \frac{34}{9} ni ayirish. Har qanday sonni noldan ayirsangiz, o‘zining manfiyi chiqadi.

$$-\frac{2}{3}x=-\frac{34}{9}$$

Ikki tarafini -\frac{3}{2} va teskari kasri -\frac{2}{3} ga ko‘paytiring.

$$x=-\frac{34}{9}\left(-\frac{3}{2}\right)$$

\frac{17}{3} hosil qilish uchun -\frac{34}{9} va -\frac{3}{2} ni ko'paytirish.

$$x=\frac{17}{3}$$