12=(1-3x)(1-3x)+(1+3x)(1+3x) eching

$$12 = ( 1 - 3 x ) ( 1 - 3 x ) + ( 1 + 3 x ) ( 1 + 3 x )$$

x uchun yechish

$$x=\frac{\sqrt{5}}{3}\approx 0,745355992$$

$$x=-\frac{\sqrt{5}}{3}\approx -0,745355992$$

Kvadrat ildizini topish bo'yicha qadamlar

\left(1-3x\right)^{2} hosil qilish uchun 1-3x va 1-3x ni ko'paytirish.

$$12=\left(1-3x\right)^{2}+\left(1+3x\right)\left(1+3x\right)$$

\left(1+3x\right)^{2} hosil qilish uchun 1+3x va 1+3x ni ko'paytirish.

$$12=\left(1-3x\right)^{2}+\left(1+3x\right)^{2}$$

\left(a-b\right)^{2}=a^{2}-2ab+b^{2} binom teoremasini \left(1-3x\right)^{2} kengaytirilishi uchun ishlating.

$$12=1-6x+9x^{2}+\left(1+3x\right)^{2}$$

\left(a+b\right)^{2}=a^{2}+2ab+b^{2} binom teoremasini \left(1+3x\right)^{2} kengaytirilishi uchun ishlating.

$$12=1-6x+9x^{2}+1+6x+9x^{2}$$

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

$$12=2-6x+9x^{2}+6x+9x^{2}$$

0 ni olish uchun -6x va 6x ni birlashtirish.

$$12=2+9x^{2}+9x^{2}$$

18x^{2} ni olish uchun 9x^{2} va 9x^{2} ni birlashtirish.

$$12=2+18x^{2}$$

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$2+18x^{2}=12$$

Ikkala tarafdan 2 ni ayirish.

$$18x^{2}=12-2$$

10 olish uchun 12 dan 2 ni ayirish.

$$18x^{2}=10$$

Ikki tarafini 18 ga bo‘ling.

$$x^{2}=\frac{10}{18}$$

\frac{10}{18} ulushini 2 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$x^{2}=\frac{5}{9}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$x=\frac{\sqrt{5}}{3} x=-\frac{\sqrt{5}}{3}$$

Kvadrat tenglamalaridan foydalanish qoidalari

\left(1-3x\right)^{2} hosil qilish uchun 1-3x va 1-3x ni ko'paytirish.

$$12=\left(1-3x\right)^{2}+\left(1+3x\right)\left(1+3x\right)$$

\left(1+3x\right)^{2} hosil qilish uchun 1+3x va 1+3x ni ko'paytirish.

$$12=\left(1-3x\right)^{2}+\left(1+3x\right)^{2}$$

\left(a-b\right)^{2}=a^{2}-2ab+b^{2} binom teoremasini \left(1-3x\right)^{2} kengaytirilishi uchun ishlating.

$$12=1-6x+9x^{2}+\left(1+3x\right)^{2}$$

\left(a+b\right)^{2}=a^{2}+2ab+b^{2} binom teoremasini \left(1+3x\right)^{2} kengaytirilishi uchun ishlating.

$$12=1-6x+9x^{2}+1+6x+9x^{2}$$

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

$$12=2-6x+9x^{2}+6x+9x^{2}$$

0 ni olish uchun -6x va 6x ni birlashtirish.

$$12=2+9x^{2}+9x^{2}$$

18x^{2} ni olish uchun 9x^{2} va 9x^{2} ni birlashtirish.

$$12=2+18x^{2}$$

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$2+18x^{2}=12$$

Ikkala tarafdan 12 ni ayirish.

$$2+18x^{2}-12=0$$

-10 olish uchun 2 dan 12 ni ayirish.

$$-10+18x^{2}=0$$

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.

$$18x^{2}-10=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 18 ni a, 0 ni b va -10 ni c bilan almashtiring.

$$x=\frac{0±\sqrt{0^{2}-4\times 18\left(-10\right)}}{2\times 18}$$

0 kvadratini chiqarish.

$$x=\frac{0±\sqrt{-4\times 18\left(-10\right)}}{2\times 18}$$

-4 ni 18 marotabaga ko'paytirish.

$$x=\frac{0±\sqrt{-72\left(-10\right)}}{2\times 18}$$

-72 ni -10 marotabaga ko'paytirish.

$$x=\frac{0±\sqrt{720}}{2\times 18}$$

720 ning kvadrat ildizini chiqarish.

$$x=\frac{0±12\sqrt{5}}{2\times 18}$$

2 ni 18 marotabaga ko'paytirish.

$$x=\frac{0±12\sqrt{5}}{36}$$

x=\frac{0±12\sqrt{5}}{36} tenglamasini yeching, bunda ± musbat.

$$x=\frac{\sqrt{5}}{3}$$

x=\frac{0±12\sqrt{5}}{36} tenglamasini yeching, bunda ± manfiy.

$$x=-\frac{\sqrt{5}}{3}$$

Tenglama yechildi.

$$x=\frac{\sqrt{5}}{3} x=-\frac{\sqrt{5}}{3}$$