(x-1)(x+1)=5(1-3x)(1+3x)+1 eching

$$(x-1)(x+1)=5(1-3x)(1+3x)+1$$

x uchun yechish

$$x=\frac{\sqrt{322}}{46}\approx 0,390094749$$

$$x=-\frac{\sqrt{322}}{46}\approx -0,390094749$$

Kvadrat ildizini topish bo'yicha qadamlar

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

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

5 ga 1-3x ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

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

5-15x ga 1+3x ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

$$x^{2}-1=5-45x^{2}+1$$

6 olish uchun 5 va 1'ni qo'shing.

$$x^{2}-1=6-45x^{2}$$

45x^{2} ni ikki tarafga qo’shing.

$$x^{2}-1+45x^{2}=6$$

46x^{2} ni olish uchun x^{2} va 45x^{2} ni birlashtirish.

$$46x^{2}-1=6$$

1 ni ikki tarafga qo’shing.

$$46x^{2}=6+1$$

7 olish uchun 6 va 1'ni qo'shing.

$$46x^{2}=7$$

Ikki tarafini 46 ga bo‘ling.

$$x^{2}=\frac{7}{46}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$x=\frac{\sqrt{322}}{46} x=-\frac{\sqrt{322}}{46}$$

Kvadrat tenglamalaridan foydalanish qoidalari

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

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

5 ga 1-3x ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

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

5-15x ga 1+3x ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

$$x^{2}-1=5-45x^{2}+1$$

6 olish uchun 5 va 1'ni qo'shing.

$$x^{2}-1=6-45x^{2}$$

Ikkala tarafdan 6 ni ayirish.

$$x^{2}-1-6=-45x^{2}$$

-7 olish uchun -1 dan 6 ni ayirish.

$$x^{2}-7=-45x^{2}$$

45x^{2} ni ikki tarafga qo’shing.

$$x^{2}-7+45x^{2}=0$$

46x^{2} ni olish uchun x^{2} va 45x^{2} ni birlashtirish.

$$46x^{2}-7=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 46 ni a, 0 ni b va -7 ni c bilan almashtiring.

$$x=\frac{0±\sqrt{0^{2}-4\times 46\left(-7\right)}}{2\times 46}$$

0 kvadratini chiqarish.

$$x=\frac{0±\sqrt{-4\times 46\left(-7\right)}}{2\times 46}$$

-4 ni 46 marotabaga ko'paytirish.

$$x=\frac{0±\sqrt{-184\left(-7\right)}}{2\times 46}$$

-184 ni -7 marotabaga ko'paytirish.

$$x=\frac{0±\sqrt{1288}}{2\times 46}$$

1288 ning kvadrat ildizini chiqarish.

$$x=\frac{0±2\sqrt{322}}{2\times 46}$$

2 ni 46 marotabaga ko'paytirish.

$$x=\frac{0±2\sqrt{322}}{92}$$

x=\frac{0±2\sqrt{322}}{92} tenglamasini yeching, bunda ± musbat.

$$x=\frac{\sqrt{322}}{46}$$

x=\frac{0±2\sqrt{322}}{92} tenglamasini yeching, bunda ± manfiy.

$$x=-\frac{\sqrt{322}}{46}$$

Tenglama yechildi.

$$x=\frac{\sqrt{322}}{46} x=-\frac{\sqrt{322}}{46}$$