(sqrt{2}x-3)(sqrt{2}x+3)=2x(x-3) eching

$$( \sqrt { 2 } x - 3 ) ( \sqrt { 2 } x + 3 ) = 2 x ( x - 3 )$$

x uchun yechish

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

Chiziqli tenglamalarni yechish bo'yicha qadamlar

Hisoblang: \left(\sqrt{2}x-3\right)\left(\sqrt{2}x+3\right). Ko‘paytirish qoida yordamida turli kvadratlarga aylantirilishi mumkin: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}. 3 kvadratini chiqarish.

$$\left(\sqrt{2}x\right)^{2}-9=2x\left(x-3\right)$$

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

$$\left(\sqrt{2}\right)^{2}x^{2}-9=2x\left(x-3\right)$$

\sqrt{2} kvadrati – 2.

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

2x ga x-3 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

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

Ikkala tarafdan 2x^{2} ni ayirish.

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

0 ni olish uchun 2x^{2} va -2x^{2} ni birlashtirish.

$$-9=-6x$$

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$-6x=-9$$

Ikki tarafini -6 ga bo‘ling.

$$x=\frac{-9}{-6}$$

\frac{-9}{-6} ulushini -3 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

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