eta_g^2=5^2+12^2 eching

$$\eta _ { g } ^ { 2 } = 5 ^ { 2 } + 12 ^ { 2 }$$

η_g uchun yechish

$$\eta _{g}=-13$$

$$\eta _{g}=13$$

Kvadratlar farqidan foydalangan qadamlar

2 daraja ko‘rsatkichini 5 ga hisoblang va 25 ni qiymatni oling.

$$\eta _{g}^{2}=25+12^{2}$$

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

$$\eta _{g}^{2}=25+144$$

169 olish uchun 25 va 144'ni qo'shing.

$$\eta _{g}^{2}=169$$

Ikkala tarafdan 169 ni ayirish.

$$\eta _{g}^{2}-169=0$$

Hisoblang: \eta _{g}^{2}-169. \eta _{g}^{2}-169 ni \eta _{g}^{2}-13^{2} sifatida qaytadan yozish. Kvadratlarning farqini ushbu formula bilan hisoblash mumkin: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(\eta _{g}-13\right)\left(\eta _{g}+13\right)=0$$

Tenglamani yechish uchun \eta _{g}-13=0 va \eta _{g}+13=0 ni yeching.

$$\eta _{g}=13 \eta _{g}=-13$$

Kvadrat ildizini topish bo'yicha qadamlar

2 daraja ko‘rsatkichini 5 ga hisoblang va 25 ni qiymatni oling.

$$\eta _{g}^{2}=25+12^{2}$$

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

$$\eta _{g}^{2}=25+144$$

169 olish uchun 25 va 144'ni qo'shing.

$$\eta _{g}^{2}=169$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\eta _{g}=13 \eta _{g}=-13$$

Kvadrat tenglamalaridan foydalanish qoidalari

2 daraja ko‘rsatkichini 5 ga hisoblang va 25 ni qiymatni oling.

$$\eta _{g}^{2}=25+12^{2}$$

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

$$\eta _{g}^{2}=25+144$$

169 olish uchun 25 va 144'ni qo'shing.

$$\eta _{g}^{2}=169$$

Ikkala tarafdan 169 ni ayirish.

$$\eta _{g}^{2}-169=0$$

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 -169 ni c bilan almashtiring.

$$\eta _{g}=\frac{0±\sqrt{0^{2}-4\left(-169\right)}}{2}$$

0 kvadratini chiqarish.

$$\eta _{g}=\frac{0±\sqrt{-4\left(-169\right)}}{2}$$

-4 ni -169 marotabaga ko'paytirish.

$$\eta _{g}=\frac{0±\sqrt{676}}{2}$$

676 ning kvadrat ildizini chiqarish.

$$\eta _{g}=\frac{0±26}{2}$$

\eta _{g}=\frac{0±26}{2} tenglamasini yeching, bunda ± musbat. 26 ni 2 ga bo'lish.

$$\eta _{g}=13$$

\eta _{g}=\frac{0±26}{2} tenglamasini yeching, bunda ± manfiy. -26 ni 2 ga bo'lish.

$$\eta _{g}=-13$$

Tenglama yechildi.

$$\eta _{g}=13 \eta _{g}=-13$$