15^2=5^2+c^2 eching

$$15 ^ { 2 } = 5 ^ { 2 } + c ^ { 2 }$$

c uchun yechish

$$c=10\sqrt{2}\approx 14,142135624$$

$$c=-10\sqrt{2}\approx -14,142135624$$

Kvadrat ildizini topish bo'yicha qadamlar

2 daraja ko‘rsatkichini 15 ga hisoblang va 225 ni qiymatni oling.

$$225=5^{2}+c^{2}$$

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

$$225=25+c^{2}$$

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$25+c^{2}=225$$

Ikkala tarafdan 25 ni ayirish.

$$c^{2}=225-25$$

200 olish uchun 225 dan 25 ni ayirish.

$$c^{2}=200$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$c=10\sqrt{2} c=-10\sqrt{2}$$

Kvadrat tenglamalaridan foydalanish qoidalari

2 daraja ko‘rsatkichini 15 ga hisoblang va 225 ni qiymatni oling.

$$225=5^{2}+c^{2}$$

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

$$225=25+c^{2}$$

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$25+c^{2}=225$$

Ikkala tarafdan 225 ni ayirish.

$$25+c^{2}-225=0$$

-200 olish uchun 25 dan 225 ni ayirish.

$$-200+c^{2}=0$$

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.

$$c^{2}-200=0$$

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 -200 ni c bilan almashtiring.

$$c=\frac{0±\sqrt{0^{2}-4\left(-200\right)}}{2}$$

0 kvadratini chiqarish.

$$c=\frac{0±\sqrt{-4\left(-200\right)}}{2}$$

-4 ni -200 marotabaga ko'paytirish.

$$c=\frac{0±\sqrt{800}}{2}$$

800 ning kvadrat ildizini chiqarish.

$$c=\frac{0±20\sqrt{2}}{2}$$

c=\frac{0±20\sqrt{2}}{2} tenglamasini yeching, bunda ± musbat.

$$c=10\sqrt{2}$$

c=\frac{0±20\sqrt{2}}{2} tenglamasini yeching, bunda ± manfiy.

$$c=-10\sqrt{2}$$

Tenglama yechildi.

$$c=10\sqrt{2} c=-10\sqrt{2}$$