1/2x-1-1/2x+1=1/4= eching

$$\frac { 1 } { 2 x - 1 } - \frac { 1 } { 2 x + 1 } = \frac { 1 } { 4 } =$$

x uchun yechish

$$x = -\frac{3}{2} = -1\frac{1}{2} = -1,5$$

$$x = \frac{3}{2} = 1\frac{1}{2} = 1,5$$

Kvadrat ildizini topish bo'yicha qadamlar

x qiymati -\frac{1}{2},\frac{1}{2} qiymatlaridan birortasiga teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. Tenglamaning ikkala tarafini 4\left(2x-1\right)\left(2x+1\right) ga, 2x-1,2x+1,4 ning eng kichik karralisiga ko‘paytiring.

$$8x+4-\left(8x-4\right)=\left(2x-1\right)\left(2x+1\right)$$

8x-4 teskarisini topish uchun har birining teskarisini toping.

$$8x+4-8x+4=\left(2x-1\right)\left(2x+1\right)$$

0 ni olish uchun 8x va -8x ni birlashtirish.

$$4+4=\left(2x-1\right)\left(2x+1\right)$$

8 olish uchun 4 va 4'ni qo'shing.

$$8=\left(2x-1\right)\left(2x+1\right)$$

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

$$8=\left(2x\right)^{2}-1$$

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

$$8=2^{2}x^{2}-1$$

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

$$8=4x^{2}-1$$

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$4x^{2}-1=8$$

1 ni ikki tarafga qo’shing.

$$4x^{2}=8+1$$

9 olish uchun 8 va 1'ni qo'shing.

$$4x^{2}=9$$

Ikki tarafini 4 ga bo‘ling.

$$x^{2}=\frac{9}{4}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

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

Kvadrat tenglamalaridan foydalanish qoidalari

x qiymati -\frac{1}{2},\frac{1}{2} qiymatlaridan birortasiga teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. Tenglamaning ikkala tarafini 4\left(2x-1\right)\left(2x+1\right) ga, 2x-1,2x+1,4 ning eng kichik karralisiga ko‘paytiring.

$$8x+4-\left(8x-4\right)=\left(2x-1\right)\left(2x+1\right)$$

8x-4 teskarisini topish uchun har birining teskarisini toping.

$$8x+4-8x+4=\left(2x-1\right)\left(2x+1\right)$$

0 ni olish uchun 8x va -8x ni birlashtirish.

$$4+4=\left(2x-1\right)\left(2x+1\right)$$

8 olish uchun 4 va 4'ni qo'shing.

$$8=\left(2x-1\right)\left(2x+1\right)$$

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

$$8=\left(2x\right)^{2}-1$$

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

$$8=2^{2}x^{2}-1$$

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

$$8=4x^{2}-1$$

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$4x^{2}-1=8$$

Ikkala tarafdan 8 ni ayirish.

$$4x^{2}-1-8=0$$

-9 olish uchun -1 dan 8 ni ayirish.

$$4x^{2}-9=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 4 ni a, 0 ni b va -9 ni c bilan almashtiring.

$$x=\frac{0±\sqrt{0^{2}-4\times 4\left(-9\right)}}{2\times 4}$$

0 kvadratini chiqarish.

$$x=\frac{0±\sqrt{-4\times 4\left(-9\right)}}{2\times 4}$$

-4 ni 4 marotabaga ko'paytirish.

$$x=\frac{0±\sqrt{-16\left(-9\right)}}{2\times 4}$$

-16 ni -9 marotabaga ko'paytirish.

$$x=\frac{0±\sqrt{144}}{2\times 4}$$

144 ning kvadrat ildizini chiqarish.

$$x=\frac{0±12}{2\times 4}$$

2 ni 4 marotabaga ko'paytirish.

$$x=\frac{0±12}{8}$$

x=\frac{0±12}{8} tenglamasini yeching, bunda ± musbat. \frac{12}{8} ulushini 4 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$x=\frac{3}{2}$$

x=\frac{0±12}{8} tenglamasini yeching, bunda ± manfiy. \frac{-12}{8} ulushini 4 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

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

Tenglama yechildi.

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