75^2+x^2=85^2 eching

$$75 ^ { 2 } + x ^ { 2 } = 85 ^ { 2 }$$

x uchun yechish

$$x=-40$$

$$x=40$$

Kvadratlar farqidan foydalangan qadamlar

2 daraja ko‘rsatkichini 75 ga hisoblang va 5625 ni qiymatni oling.

$$5625+x^{2}=85^{2}$$

2 daraja ko‘rsatkichini 85 ga hisoblang va 7225 ni qiymatni oling.

$$5625+x^{2}=7225$$

Ikkala tarafdan 7225 ni ayirish.

$$5625+x^{2}-7225=0$$

-1600 olish uchun 5625 dan 7225 ni ayirish.

$$-1600+x^{2}=0$$

Hisoblang: -1600+x^{2}. -1600+x^{2} ni x^{2}-40^{2} sifatida qaytadan yozish. Kvadratlarning farqini ushbu formula bilan hisoblash mumkin: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(x-40\right)\left(x+40\right)=0$$

Tenglamani yechish uchun x-40=0 va x+40=0 ni yeching.

$$x=40 x=-40$$

Kvadrat ildizini topish bo'yicha qadamlar

2 daraja ko‘rsatkichini 75 ga hisoblang va 5625 ni qiymatni oling.

$$5625+x^{2}=85^{2}$$

2 daraja ko‘rsatkichini 85 ga hisoblang va 7225 ni qiymatni oling.

$$5625+x^{2}=7225$$

Ikkala tarafdan 5625 ni ayirish.

$$x^{2}=7225-5625$$

1600 olish uchun 7225 dan 5625 ni ayirish.

$$x^{2}=1600$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$x=40 x=-40$$

Kvadrat tenglamalaridan foydalanish qoidalari

2 daraja ko‘rsatkichini 75 ga hisoblang va 5625 ni qiymatni oling.

$$5625+x^{2}=85^{2}$$

2 daraja ko‘rsatkichini 85 ga hisoblang va 7225 ni qiymatni oling.

$$5625+x^{2}=7225$$

Ikkala tarafdan 7225 ni ayirish.

$$5625+x^{2}-7225=0$$

-1600 olish uchun 5625 dan 7225 ni ayirish.

$$-1600+x^{2}=0$$

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.

$$x^{2}-1600=0$$

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 -1600 ni c bilan almashtiring.

$$x=\frac{0±\sqrt{0^{2}-4\left(-1600\right)}}{2}$$

0 kvadratini chiqarish.

$$x=\frac{0±\sqrt{-4\left(-1600\right)}}{2}$$

-4 ni -1600 marotabaga ko'paytirish.

$$x=\frac{0±\sqrt{6400}}{2}$$

6400 ning kvadrat ildizini chiqarish.

$$x=\frac{0±80}{2}$$

x=\frac{0±80}{2} tenglamasini yeching, bunda ± musbat. 80 ni 2 ga bo'lish.

$$x=40$$

x=\frac{0±80}{2} tenglamasini yeching, bunda ± manfiy. -80 ni 2 ga bo'lish.

$$x=-40$$

Tenglama yechildi.

$$x=40 x=-40$$