(5x+1)(5x-1)=[1] eching

$$( 5 x + 1 ) ( 5 x - 1 ) = [ 1 ]$$

x uchun yechish

$$x=\frac{\sqrt{2}}{5}\approx 0,282842712$$

$$x=-\frac{\sqrt{2}}{5}\approx -0,282842712$$

Kvadrat ildizini topish bo'yicha qadamlar

Hisoblang: \left(5x+1\right)\left(5x-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.

$$\left(5x\right)^{2}-1=1$$

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

$$5^{2}x^{2}-1=1$$

2 daraja ko‘rsatkichini 5 ga hisoblang va 25 ni qiymatni oling.

$$25x^{2}-1=1$$

1 ni ikki tarafga qo’shing.

$$25x^{2}=1+1$$

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

$$25x^{2}=2$$

Ikki tarafini 25 ga bo‘ling.

$$x^{2}=\frac{2}{25}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$x=\frac{\sqrt{2}}{5} x=-\frac{\sqrt{2}}{5}$$

Kvadrat tenglamalaridan foydalanish qoidalari

Hisoblang: \left(5x+1\right)\left(5x-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.

$$\left(5x\right)^{2}-1=1$$

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

$$5^{2}x^{2}-1=1$$

2 daraja ko‘rsatkichini 5 ga hisoblang va 25 ni qiymatni oling.

$$25x^{2}-1=1$$

Ikkala tarafdan 1 ni ayirish.

$$25x^{2}-1-1=0$$

-2 olish uchun -1 dan 1 ni ayirish.

$$25x^{2}-2=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 25 ni a, 0 ni b va -2 ni c bilan almashtiring.

$$x=\frac{0±\sqrt{0^{2}-4\times 25\left(-2\right)}}{2\times 25}$$

0 kvadratini chiqarish.

$$x=\frac{0±\sqrt{-4\times 25\left(-2\right)}}{2\times 25}$$

-4 ni 25 marotabaga ko'paytirish.

$$x=\frac{0±\sqrt{-100\left(-2\right)}}{2\times 25}$$

-100 ni -2 marotabaga ko'paytirish.

$$x=\frac{0±\sqrt{200}}{2\times 25}$$

200 ning kvadrat ildizini chiqarish.

$$x=\frac{0±10\sqrt{2}}{2\times 25}$$

2 ni 25 marotabaga ko'paytirish.

$$x=\frac{0±10\sqrt{2}}{50}$$

x=\frac{0±10\sqrt{2}}{50} tenglamasini yeching, bunda ± musbat.

$$x=\frac{\sqrt{2}}{5}$$

x=\frac{0±10\sqrt{2}}{50} tenglamasini yeching, bunda ± manfiy.

$$x=-\frac{\sqrt{2}}{5}$$

Tenglama yechildi.

$$x=\frac{\sqrt{2}}{5} x=-\frac{\sqrt{2}}{5}$$