(1/x+1/x)^2=1 eching

$$( \frac { 1 } { x } + \frac { 1 } { x } ) ^ { 2 } = 1$$

x uchun yechish

$$x=-2$$

$$x=2$$

Kvadrat ildizini topish bo'yicha qadamlar

2\times \frac{1}{x} ni olish uchun \frac{1}{x} va \frac{1}{x} ni birlashtirish.

$$\left(2\times \frac{1}{x}\right)^{2}=1$$

2\times \frac{1}{x} ni yagona kasrga aylantiring.

$$\left(\frac{2}{x}\right)^{2}=1$$

\frac{2}{x}ni darajaga oshirish uchun, surat va maxrajni darajaga oshirib, keyin bo‘ling.

$$\frac{2^{2}}{x^{2}}=1$$

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

$$\frac{4}{x^{2}}=1$$

x qiymati 0 teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. Tenglamaning ikkala tarafini x^{2} ga ko'paytirish.

$$4=x^{2}$$

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$x^{2}=4$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$x=2 x=-2$$

Kvadrat tenglamalaridan foydalanish qoidalari

2\times \frac{1}{x} ni olish uchun \frac{1}{x} va \frac{1}{x} ni birlashtirish.

$$\left(2\times \frac{1}{x}\right)^{2}=1$$

2\times \frac{1}{x} ni yagona kasrga aylantiring.

$$\left(\frac{2}{x}\right)^{2}=1$$

\frac{2}{x}ni darajaga oshirish uchun, surat va maxrajni darajaga oshirib, keyin bo‘ling.

$$\frac{2^{2}}{x^{2}}=1$$

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

$$\frac{4}{x^{2}}=1$$

Ikkala tarafdan 1 ni ayirish.

$$\frac{4}{x^{2}}-1=0$$

Ifodalarni qo‘shish yoki ayirish uchun ularni yoyib, maxrajlarini bir xil qiling. 1 ni \frac{x^{2}}{x^{2}} marotabaga ko'paytirish.

$$\frac{4}{x^{2}}-\frac{x^{2}}{x^{2}}=0$$

\frac{4}{x^{2}} va \frac{x^{2}}{x^{2}} da bir xil maxraji bor, ularning suratini ayirish orqali ayiring.

$$\frac{4-x^{2}}{x^{2}}=0$$

x qiymati 0 teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. Tenglamaning ikkala tarafini x^{2} ga ko'paytirish.

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

Bu kabi kvadrat tenglamalarni x^{2} sharti bilan, biroq x shartisiz hamon kvadrat tenglamasidan foydalanib yechish mumkin, \frac{-b±\sqrt{b^{2}-4ac}}{2a}, ular standart formulaga solingandan so'ng: ax^{2}+bx+c=0.

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

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} -1 ni a, 0 ni b va 4 ni c bilan almashtiring.

$$x=\frac{0±\sqrt{0^{2}-4\left(-1\right)\times 4}}{2\left(-1\right)}$$

0 kvadratini chiqarish.

$$x=\frac{0±\sqrt{-4\left(-1\right)\times 4}}{2\left(-1\right)}$$

-4 ni -1 marotabaga ko'paytirish.

$$x=\frac{0±\sqrt{4\times 4}}{2\left(-1\right)}$$

4 ni 4 marotabaga ko'paytirish.

$$x=\frac{0±\sqrt{16}}{2\left(-1\right)}$$

16 ning kvadrat ildizini chiqarish.

$$x=\frac{0±4}{2\left(-1\right)}$$

2 ni -1 marotabaga ko'paytirish.

$$x=\frac{0±4}{-2}$$

x=\frac{0±4}{-2} tenglamasini yeching, bunda ± musbat. 4 ni -2 ga bo'lish.

$$x=-2$$

x=\frac{0±4}{-2} tenglamasini yeching, bunda ± manfiy. -4 ni -2 ga bo'lish.

$$x=2$$

Tenglama yechildi.

$$x=-2 x=2$$