25x^2-1=0 eching

$$25 x ^ { 2 } - 1 = 0$$

x uchun yechish

$$x=\frac{1}{5}=0,2$$

$$x=-\frac{1}{5}=-0,2$$

Kvadratlar farqidan foydalangan qadamlar

Hisoblang: 25x^{2}-1. 25x^{2}-1 ni \left(5x\right)^{2}-1^{2} sifatida qaytadan yozish. Kvadratlarning farqini ushbu formula bilan hisoblash mumkin: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(5x-1\right)\left(5x+1\right)=0$$

Tenglamani yechish uchun 5x-1=0 va 5x+1=0 ni yeching.

$$x=\frac{1}{5} x=-\frac{1}{5}$$

Kvadrat ildizini topish bo'yicha qadamlar

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

$$25x^{2}=1$$

Ikki tarafini 25 ga bo‘ling.

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

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$x=\frac{1}{5} x=-\frac{1}{5}$$

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.

$$25x^{2}-1=0$$

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

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

0 kvadratini chiqarish.

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

-4 ni 25 marotabaga ko'paytirish.

$$x=\frac{0±\sqrt{-100\left(-1\right)}}{2\times 25}$$

-100 ni -1 marotabaga ko'paytirish.

$$x=\frac{0±\sqrt{100}}{2\times 25}$$

100 ning kvadrat ildizini chiqarish.

$$x=\frac{0±10}{2\times 25}$$

2 ni 25 marotabaga ko'paytirish.

$$x=\frac{0±10}{50}$$

x=\frac{0±10}{50} tenglamasini yeching, bunda ± musbat. \frac{10}{50} ulushini 10 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$x=\frac{1}{5}$$

x=\frac{0±10}{50} tenglamasini yeching, bunda ± manfiy. \frac{-10}{50} ulushini 10 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$x=-\frac{1}{5}$$

Tenglama yechildi.

$$x=\frac{1}{5} x=-\frac{1}{5}$$