3^2+x^2=4^2 eching

$$3 ^ { 2 } + x ^ { 2 } = 4 ^ { 2 }$$

x uchun yechish

$$x=\sqrt{7}\approx 2,645751311$$

$$x=-\sqrt{7}\approx -2,645751311$$

Kvadrat ildizini topish bo'yicha qadamlar

2 daraja ko‘rsatkichini 3 ga hisoblang va 9 ni qiymatni oling.

$$9+x^{2}=4^{2}$$

2 daraja ko‘rsatkichini 4 ga hisoblang va 16 ni qiymatni oling.

$$9+x^{2}=16$$

Ikkala tarafdan 9 ni ayirish.

$$x^{2}=16-9$$

7 olish uchun 16 dan 9 ni ayirish.

$$x^{2}=7$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

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

Kvadrat tenglamalaridan foydalanish qoidalari

2 daraja ko‘rsatkichini 3 ga hisoblang va 9 ni qiymatni oling.

$$9+x^{2}=4^{2}$$

2 daraja ko‘rsatkichini 4 ga hisoblang va 16 ni qiymatni oling.

$$9+x^{2}=16$$

Ikkala tarafdan 16 ni ayirish.

$$9+x^{2}-16=0$$

-7 olish uchun 9 dan 16 ni ayirish.

$$-7+x^{2}=0$$

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.

$$x^{2}-7=0$$

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 -7 ni c bilan almashtiring.

$$x=\frac{0±\sqrt{0^{2}-4\left(-7\right)}}{2}$$

0 kvadratini chiqarish.

$$x=\frac{0±\sqrt{-4\left(-7\right)}}{2}$$

-4 ni -7 marotabaga ko'paytirish.

$$x=\frac{0±\sqrt{28}}{2}$$

28 ning kvadrat ildizini chiqarish.

$$x=\frac{0±2\sqrt{7}}{2}$$

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

$$x=\sqrt{7}$$

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

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

Tenglama yechildi.

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