(5x-2)^2=5x^2-20x+4 eching

$$( 5 x - 2 ) ^ { 2 } = 5 x ^ { 2 } - 20 x + 4$$

x uchun yechish

$$x=0$$

Kvadrat ildizini topish bo'yicha qadamlar

\left(a-b\right)^{2}=a^{2}-2ab+b^{2} binom teoremasini \left(5x-2\right)^{2} kengaytirilishi uchun ishlating.

$$25x^{2}-20x+4=5x^{2}-20x+4$$

Ikkala tarafdan 5x^{2} ni ayirish.

$$25x^{2}-20x+4-5x^{2}=-20x+4$$

20x^{2} ni olish uchun 25x^{2} va -5x^{2} ni birlashtirish.

$$20x^{2}-20x+4=-20x+4$$

20x ni ikki tarafga qo’shing.

$$20x^{2}-20x+4+20x=4$$

0 ni olish uchun -20x va 20x ni birlashtirish.

$$20x^{2}+4=4$$

Ikkala tarafdan 4 ni ayirish.

$$20x^{2}=4-4$$

0 olish uchun 4 dan 4 ni ayirish.

$$20x^{2}=0$$

Ikki tarafini 20 ga bo‘ling. Nol bo‘lmagan har qanday sonni nolga ko‘paytirsangiz, nol bo‘ladi.

$$x^{2}=0$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$x=0 x=0$$

Tenglama yechildi. Yechimlar bir xil.

$$x=0$$

Kvadrat tenglamalaridan foydalanish qoidalari

\left(a-b\right)^{2}=a^{2}-2ab+b^{2} binom teoremasini \left(5x-2\right)^{2} kengaytirilishi uchun ishlating.

$$25x^{2}-20x+4=5x^{2}-20x+4$$

Ikkala tarafdan 5x^{2} ni ayirish.

$$25x^{2}-20x+4-5x^{2}=-20x+4$$

20x^{2} ni olish uchun 25x^{2} va -5x^{2} ni birlashtirish.

$$20x^{2}-20x+4=-20x+4$$

20x ni ikki tarafga qo’shing.

$$20x^{2}-20x+4+20x=4$$

0 ni olish uchun -20x va 20x ni birlashtirish.

$$20x^{2}+4=4$$

Ikkala tarafdan 4 ni ayirish.

$$20x^{2}+4-4=0$$

0 olish uchun 4 dan 4 ni ayirish.

$$20x^{2}=0$$

Ikki tarafini 20 ga bo‘ling. Nol bo‘lmagan har qanday sonni nolga ko‘paytirsangiz, nol bo‘ladi.

$$x^{2}=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 1 ni a, 0 ni b va 0 ni c bilan almashtiring.

$$x=\frac{0±\sqrt{0^{2}}}{2}$$

0^{2} ning kvadrat ildizini chiqarish.

$$x=\frac{0±0}{2}$$

0 ni 2 ga bo'lish.

$$x=0$$