a^2+20^2=25^2 eching

$$a ^ { 2 } + 20 ^ { 2 } = 25 ^ { 2 }$$

a uchun yechish

$$a=-15$$

$$a=15$$

Kvadratlar farqidan foydalangan qadamlar

2 daraja ko‘rsatkichini 20 ga hisoblang va 400 ni qiymatni oling.

$$a^{2}+400=25^{2}$$

2 daraja ko‘rsatkichini 25 ga hisoblang va 625 ni qiymatni oling.

$$a^{2}+400=625$$

Ikkala tarafdan 625 ni ayirish.

$$a^{2}+400-625=0$$

-225 olish uchun 400 dan 625 ni ayirish.

$$a^{2}-225=0$$

Hisoblang: a^{2}-225. a^{2}-225 ni a^{2}-15^{2} sifatida qaytadan yozish. Kvadratlarning farqini ushbu formula bilan hisoblash mumkin: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(a-15\right)\left(a+15\right)=0$$

Tenglamani yechish uchun a-15=0 va a+15=0 ni yeching.

$$a=15 a=-15$$

Kvadrat ildizini topish bo'yicha qadamlar

2 daraja ko‘rsatkichini 20 ga hisoblang va 400 ni qiymatni oling.

$$a^{2}+400=25^{2}$$

2 daraja ko‘rsatkichini 25 ga hisoblang va 625 ni qiymatni oling.

$$a^{2}+400=625$$

Ikkala tarafdan 400 ni ayirish.

$$a^{2}=625-400$$

225 olish uchun 625 dan 400 ni ayirish.

$$a^{2}=225$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$a=15 a=-15$$

Kvadrat tenglamalaridan foydalanish qoidalari

2 daraja ko‘rsatkichini 20 ga hisoblang va 400 ni qiymatni oling.

$$a^{2}+400=25^{2}$$

2 daraja ko‘rsatkichini 25 ga hisoblang va 625 ni qiymatni oling.

$$a^{2}+400=625$$

Ikkala tarafdan 625 ni ayirish.

$$a^{2}+400-625=0$$

-225 olish uchun 400 dan 625 ni ayirish.

$$a^{2}-225=0$$

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 -225 ni c bilan almashtiring.

$$a=\frac{0±\sqrt{0^{2}-4\left(-225\right)}}{2}$$

0 kvadratini chiqarish.

$$a=\frac{0±\sqrt{-4\left(-225\right)}}{2}$$

-4 ni -225 marotabaga ko'paytirish.

$$a=\frac{0±\sqrt{900}}{2}$$

900 ning kvadrat ildizini chiqarish.

$$a=\frac{0±30}{2}$$

a=\frac{0±30}{2} tenglamasini yeching, bunda ± musbat. 30 ni 2 ga bo'lish.

$$a=15$$

a=\frac{0±30}{2} tenglamasini yeching, bunda ± manfiy. -30 ni 2 ga bo'lish.

$$a=-15$$

Tenglama yechildi.

$$a=15 a=-15$$