x^2-4900=0 eching

$$x ^ { 2 } - 4900 = 0$$

x uchun yechish

$$x=70$$

$$x=-70$$

Kvadratlar farqidan foydalangan qadamlar

Hisoblang: x^{2}-4900. x^{2}-4900 ni x^{2}-70^{2} sifatida qaytadan yozish. Kvadratlarning farqini ushbu formula bilan hisoblash mumkin: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(x-70\right)\left(x+70\right)=0$$

Tenglamani yechish uchun x-70=0 va x+70=0 ni yeching.

$$x=70 x=-70$$

Kvadrat ildizini topish bo'yicha qadamlar

4900 ni ikki tarafga qo’shing. Har qanday songa nolni qo‘shsangiz, o‘zi chiqadi.

$$x^{2}=4900$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$x=70 x=-70$$

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.

$$x^{2}-4900=0$$

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 -4900 ni c bilan almashtiring.

$$x=\frac{0±\sqrt{0^{2}-4\left(-4900\right)}}{2}$$

0 kvadratini chiqarish.

$$x=\frac{0±\sqrt{-4\left(-4900\right)}}{2}$$

-4 ni -4900 marotabaga ko'paytirish.

$$x=\frac{0±\sqrt{19600}}{2}$$

19600 ning kvadrat ildizini chiqarish.

$$x=\frac{0±140}{2}$$

x=\frac{0±140}{2} tenglamasini yeching, bunda ± musbat. 140 ni 2 ga bo'lish.

$$x=70$$

x=\frac{0±140}{2} tenglamasini yeching, bunda ± manfiy. -140 ni 2 ga bo'lish.

$$x=-70$$

Tenglama yechildi.

$$x=70 x=-70$$