25/4x^2-1=0 eching

$$\frac { 25 } { 4 } x ^ { 2 } - 1 = 0$$

x uchun yechish

$$x=\frac{2}{5}=0,4$$

$$x=-\frac{2}{5}=-0,4$$

Kvadratlar farqidan foydalangan qadamlar

Ikkala tarafini 4 ga ko‘paytiring.

$$25x^{2}-4=0$$

Hisoblang: 25x^{2}-4. 25x^{2}-4 ni \left(5x\right)^{2}-2^{2} sifatida qaytadan yozish. Kvadratlarning farqini ushbu formula bilan hisoblash mumkin: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(5x-2\right)\left(5x+2\right)=0$$

Tenglamani yechish uchun 5x-2=0 va 5x+2=0 ni yeching.

$$x=\frac{2}{5} x=-\frac{2}{5}$$

Kvadrat ildizini topish bo'yicha qadamlar

1 ni ikki tarafga qo’shing. Har qanday songa nolni qo‘shsangiz, o‘zi chiqadi.

$$\frac{25}{4}x^{2}=1$$

Ikki tarafini \frac{4}{25} va teskari kasri \frac{25}{4} ga ko‘paytiring.

$$x^{2}=1\times \frac{4}{25}$$

\frac{4}{25} hosil qilish uchun 1 va \frac{4}{25} ni ko'paytirish.

$$x^{2}=\frac{4}{25}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$x=\frac{2}{5} x=-\frac{2}{5}$$

Kvadrat tenglamalaridan foydalanish qoidalari

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.

$$\frac{25}{4}x^{2}-1=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} \frac{25}{4} ni a, 0 ni b va -1 ni c bilan almashtiring.

$$x=\frac{0±\sqrt{0^{2}-4\times \frac{25}{4}\left(-1\right)}}{2\times \frac{25}{4}}$$

0 kvadratini chiqarish.

$$x=\frac{0±\sqrt{-4\times \frac{25}{4}\left(-1\right)}}{2\times \frac{25}{4}}$$

-4 ni \frac{25}{4} marotabaga ko'paytirish.

$$x=\frac{0±\sqrt{-25\left(-1\right)}}{2\times \frac{25}{4}}$$

-25 ni -1 marotabaga ko'paytirish.

$$x=\frac{0±\sqrt{25}}{2\times \frac{25}{4}}$$

25 ning kvadrat ildizini chiqarish.

$$x=\frac{0±5}{2\times \frac{25}{4}}$$

2 ni \frac{25}{4} marotabaga ko'paytirish.

$$x=\frac{0±5}{\frac{25}{2}}$$

x=\frac{0±5}{\frac{25}{2}} tenglamasini yeching, bunda ± musbat. 5 ni \frac{25}{2} ga bo'lish 5 ga k'paytirish \frac{25}{2} ga qaytarish.

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

x=\frac{0±5}{\frac{25}{2}} tenglamasini yeching, bunda ± manfiy. -5 ni \frac{25}{2} ga bo'lish -5 ga k'paytirish \frac{25}{2} ga qaytarish.

$$x=-\frac{2}{5}$$

Tenglama yechildi.

$$x=\frac{2}{5} x=-\frac{2}{5}$$