x^2+12^2=16^2 eching

$${ x }^{ 2 } + { 12 }^{ 2 } = { 16 }^{ 2 }$$

x uchun yechish

$$x=4\sqrt{7}\approx 10,583005244$$

$$x=-4\sqrt{7}\approx -10,583005244$$

Kvadrat ildizini topish bo'yicha qadamlar

2 daraja ko‘rsatkichini 12 ga hisoblang va 144 ni qiymatni oling.

$$x^{2}+144=16^{2}$$

2 daraja ko‘rsatkichini 16 ga hisoblang va 256 ni qiymatni oling.

$$x^{2}+144=256$$

Ikkala tarafdan 144 ni ayirish.

$$x^{2}=256-144$$

112 olish uchun 256 dan 144 ni ayirish.

$$x^{2}=112$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$x=4\sqrt{7} x=-4\sqrt{7}$$

Kvadrat tenglamalaridan foydalanish qoidalari

2 daraja ko‘rsatkichini 12 ga hisoblang va 144 ni qiymatni oling.

$$x^{2}+144=16^{2}$$

2 daraja ko‘rsatkichini 16 ga hisoblang va 256 ni qiymatni oling.

$$x^{2}+144=256$$

Ikkala tarafdan 256 ni ayirish.

$$x^{2}+144-256=0$$

-112 olish uchun 144 dan 256 ni ayirish.

$$x^{2}-112=0$$

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 -112 ni c bilan almashtiring.

$$x=\frac{0±\sqrt{0^{2}-4\left(-112\right)}}{2}$$

0 kvadratini chiqarish.

$$x=\frac{0±\sqrt{-4\left(-112\right)}}{2}$$

-4 ni -112 marotabaga ko'paytirish.

$$x=\frac{0±\sqrt{448}}{2}$$

448 ning kvadrat ildizini chiqarish.

$$x=\frac{0±8\sqrt{7}}{2}$$

x=\frac{0±8\sqrt{7}}{2} tenglamasini yeching, bunda ± musbat.

$$x=4\sqrt{7}$$

x=\frac{0±8\sqrt{7}}{2} tenglamasini yeching, bunda ± manfiy.

$$x=-4\sqrt{7}$$

Tenglama yechildi.

$$x=4\sqrt{7} x=-4\sqrt{7}$$