80^2+x^2=82^2 eching

$$80 ^ { 2 } + x ^ { 2 } = 82 ^ { 2 }$$

x uchun yechish

$$x=-18$$

$$x=18$$

Kvadratlar farqidan foydalangan qadamlar

2 daraja ko‘rsatkichini 80 ga hisoblang va 6400 ni qiymatni oling.

$$6400+x^{2}=82^{2}$$

2 daraja ko‘rsatkichini 82 ga hisoblang va 6724 ni qiymatni oling.

$$6400+x^{2}=6724$$

Ikkala tarafdan 6724 ni ayirish.

$$6400+x^{2}-6724=0$$

-324 olish uchun 6400 dan 6724 ni ayirish.

$$-324+x^{2}=0$$

Hisoblang: -324+x^{2}. -324+x^{2} ni x^{2}-18^{2} sifatida qaytadan yozish. Kvadratlarning farqini ushbu formula bilan hisoblash mumkin: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(x-18\right)\left(x+18\right)=0$$

Tenglamani yechish uchun x-18=0 va x+18=0 ni yeching.

$$x=18 x=-18$$

Kvadrat ildizini topish bo'yicha qadamlar

2 daraja ko‘rsatkichini 80 ga hisoblang va 6400 ni qiymatni oling.

$$6400+x^{2}=82^{2}$$

2 daraja ko‘rsatkichini 82 ga hisoblang va 6724 ni qiymatni oling.

$$6400+x^{2}=6724$$

Ikkala tarafdan 6400 ni ayirish.

$$x^{2}=6724-6400$$

324 olish uchun 6724 dan 6400 ni ayirish.

$$x^{2}=324$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$x=18 x=-18$$

Kvadrat tenglamalaridan foydalanish qoidalari

2 daraja ko‘rsatkichini 80 ga hisoblang va 6400 ni qiymatni oling.

$$6400+x^{2}=82^{2}$$

2 daraja ko‘rsatkichini 82 ga hisoblang va 6724 ni qiymatni oling.

$$6400+x^{2}=6724$$

Ikkala tarafdan 6724 ni ayirish.

$$6400+x^{2}-6724=0$$

-324 olish uchun 6400 dan 6724 ni ayirish.

$$-324+x^{2}=0$$

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.

$$x^{2}-324=0$$

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 -324 ni c bilan almashtiring.

$$x=\frac{0±\sqrt{0^{2}-4\left(-324\right)}}{2}$$

0 kvadratini chiqarish.

$$x=\frac{0±\sqrt{-4\left(-324\right)}}{2}$$

-4 ni -324 marotabaga ko'paytirish.

$$x=\frac{0±\sqrt{1296}}{2}$$

1296 ning kvadrat ildizini chiqarish.

$$x=\frac{0±36}{2}$$

x=\frac{0±36}{2} tenglamasini yeching, bunda ± musbat. 36 ni 2 ga bo'lish.

$$x=18$$

x=\frac{0±36}{2} tenglamasini yeching, bunda ± manfiy. -36 ni 2 ga bo'lish.

$$x=-18$$

Tenglama yechildi.

$$x=18 x=-18$$