(9x+1)(9x-1)=1 eching

$$( 9 x + 1 ) ( 9 x - 1 ) = 1$$

x uchun yechish

$$x=\frac{\sqrt{2}}{9}\approx 0,15713484$$

$$x=-\frac{\sqrt{2}}{9}\approx -0,15713484$$

Kvadrat ildizini topish bo'yicha qadamlar

Hisoblang: \left(9x+1\right)\left(9x-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.

$$\left(9x\right)^{2}-1=1$$

\left(9x\right)^{2} ni kengaytirish.

$$9^{2}x^{2}-1=1$$

2 daraja ko‘rsatkichini 9 ga hisoblang va 81 ni qiymatni oling.

$$81x^{2}-1=1$$

1 ni ikki tarafga qo’shing.

$$81x^{2}=1+1$$

2 olish uchun 1 va 1'ni qo'shing.

$$81x^{2}=2$$

Ikki tarafini 81 ga bo‘ling.

$$x^{2}=\frac{2}{81}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$x=\frac{\sqrt{2}}{9} x=-\frac{\sqrt{2}}{9}$$

Kvadrat tenglamalaridan foydalanish qoidalari

Hisoblang: \left(9x+1\right)\left(9x-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.

$$\left(9x\right)^{2}-1=1$$

\left(9x\right)^{2} ni kengaytirish.

$$9^{2}x^{2}-1=1$$

2 daraja ko‘rsatkichini 9 ga hisoblang va 81 ni qiymatni oling.

$$81x^{2}-1=1$$

Ikkala tarafdan 1 ni ayirish.

$$81x^{2}-1-1=0$$

-2 olish uchun -1 dan 1 ni ayirish.

$$81x^{2}-2=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 81 ni a, 0 ni b va -2 ni c bilan almashtiring.

$$x=\frac{0±\sqrt{0^{2}-4\times 81\left(-2\right)}}{2\times 81}$$

0 kvadratini chiqarish.

$$x=\frac{0±\sqrt{-4\times 81\left(-2\right)}}{2\times 81}$$

-4 ni 81 marotabaga ko'paytirish.

$$x=\frac{0±\sqrt{-324\left(-2\right)}}{2\times 81}$$

-324 ni -2 marotabaga ko'paytirish.

$$x=\frac{0±\sqrt{648}}{2\times 81}$$

648 ning kvadrat ildizini chiqarish.

$$x=\frac{0±18\sqrt{2}}{2\times 81}$$

2 ni 81 marotabaga ko'paytirish.

$$x=\frac{0±18\sqrt{2}}{162}$$

x=\frac{0±18\sqrt{2}}{162} tenglamasini yeching, bunda ± musbat.

$$x=\frac{\sqrt{2}}{9}$$

x=\frac{0±18\sqrt{2}}{162} tenglamasini yeching, bunda ± manfiy.

$$x=-\frac{\sqrt{2}}{9}$$

Tenglama yechildi.

$$x=\frac{\sqrt{2}}{9} x=-\frac{\sqrt{2}}{9}$$