(2x-1)*(2x+1)=12x-10 eching

$$(2x-1) \times (2x+1)=12x-10$$

x uchun yechish

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

Kvadrat tenglamalaridan foydalanish qoidalari

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.

$$\left(2x\right)^{2}-1=12x-10$$

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

$$2^{2}x^{2}-1=12x-10$$

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

$$4x^{2}-1=12x-10$$

Ikkala tarafdan 12x ni ayirish.

$$4x^{2}-1-12x=-10$$

10 ni ikki tarafga qo’shing.

$$4x^{2}-1-12x+10=0$$

9 olish uchun -1 va 10'ni qo'shing.

$$4x^{2}+9-12x=0$$

ax^{2}+bx+c=0 shaklidagi barcha tenglamalarni kvadrat formulasi bilan yechish mumkin: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. Kvadrat formula ikki yechmni taqdim qiladi, biri ± qo'shish bo'lganda, va ikkinchisi ayiruv bo'lganda.

$$4x^{2}-12x+9=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 4 ni a, -12 ni b va 9 ni c bilan almashtiring.

$$x=\frac{-\left(-12\right)±\sqrt{\left(-12\right)^{2}-4\times 4\times 9}}{2\times 4}$$

-12 kvadratini chiqarish.

$$x=\frac{-\left(-12\right)±\sqrt{144-4\times 4\times 9}}{2\times 4}$$

-4 ni 4 marotabaga ko'paytirish.

$$x=\frac{-\left(-12\right)±\sqrt{144-16\times 9}}{2\times 4}$$

-16 ni 9 marotabaga ko'paytirish.

$$x=\frac{-\left(-12\right)±\sqrt{144-144}}{2\times 4}$$

144 ni -144 ga qo'shish.

$$x=\frac{-\left(-12\right)±\sqrt{0}}{2\times 4}$$

0 ning kvadrat ildizini chiqarish.

$$x=-\frac{-12}{2\times 4}$$

-12 ning teskarisi 12 ga teng.

$$x=\frac{12}{2\times 4}$$

2 ni 4 marotabaga ko'paytirish.

$$x=\frac{12}{8}$$

\frac{12}{8} ulushini 4 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

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

Kvadratni yakunlash bo'yicha qadamlar

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.

$$\left(2x\right)^{2}-1=12x-10$$

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

$$2^{2}x^{2}-1=12x-10$$

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

$$4x^{2}-1=12x-10$$

Ikkala tarafdan 12x ni ayirish.

$$4x^{2}-1-12x=-10$$

1 ni ikki tarafga qo’shing.

$$4x^{2}-12x=-10+1$$

-9 olish uchun -10 va 1'ni qo'shing.

$$4x^{2}-12x=-9$$

Ikki tarafini 4 ga bo‘ling.

$$\frac{4x^{2}-12x}{4}=-\frac{9}{4}$$

4 ga bo'lish 4 ga ko'paytirishni bekor qiladi.

$$x^{2}+\left(-\frac{12}{4}\right)x=-\frac{9}{4}$$

-12 ni 4 ga bo'lish.

$$x^{2}-3x=-\frac{9}{4}$$

-3 ni bo‘lish, x shartining koeffitsienti, 2 ga -\frac{3}{2} olish uchun. Keyin, -\frac{3}{2} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}-3x+\left(-\frac{3}{2}\right)^{2}=-\frac{9}{4}+\left(-\frac{3}{2}\right)^{2}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib -\frac{3}{2} kvadratini chiqarish.

$$x^{2}-3x+\frac{9}{4}=\frac{-9+9}{4}$$

Umumiy maxrajni topib va hisoblovchini qo'shish orqali -\frac{9}{4} ni \frac{9}{4} ga qo'shing. So'ngra agar imkoni bo'lsa kasrni eng kam shartga qisqartiring.

$$x^{2}-3x+\frac{9}{4}=0$$

x^{2}-3x+\frac{9}{4} omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x-\frac{3}{2}\right)^{2}=0$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-\frac{3}{2}\right)^{2}}=\sqrt{0}$$

Qisqartirish.

$$x-\frac{3}{2}=0 x-\frac{3}{2}=0$$

\frac{3}{2} ni tenglamaning ikkala tarafiga qo'shish.

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

Tenglama yechildi. Yechimlar bir xil.

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