20^2+x^2=24^2 eching

$$20 ^ { 2 } + x ^ { 2 } = 24 ^ { 2 }$$

x uchun yechish

$$x=4\sqrt{11}\approx 13,266499161$$

$$x=-4\sqrt{11}\approx -13,266499161$$

Kvadrat ildizini topish bo'yicha qadamlar

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

$$400+x^{2}=24^{2}$$

2 daraja ko‘rsatkichini 24 ga hisoblang va 576 ni qiymatni oling.

$$400+x^{2}=576$$

Ikkala tarafdan 400 ni ayirish.

$$x^{2}=576-400$$

176 olish uchun 576 dan 400 ni ayirish.

$$x^{2}=176$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$x=4\sqrt{11} x=-4\sqrt{11}$$

Kvadrat tenglamalaridan foydalanish qoidalari

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

$$400+x^{2}=24^{2}$$

2 daraja ko‘rsatkichini 24 ga hisoblang va 576 ni qiymatni oling.

$$400+x^{2}=576$$

Ikkala tarafdan 576 ni ayirish.

$$400+x^{2}-576=0$$

-176 olish uchun 400 dan 576 ni ayirish.

$$-176+x^{2}=0$$

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.

$$x^{2}-176=0$$

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 -176 ni c bilan almashtiring.

$$x=\frac{0±\sqrt{0^{2}-4\left(-176\right)}}{2}$$

0 kvadratini chiqarish.

$$x=\frac{0±\sqrt{-4\left(-176\right)}}{2}$$

-4 ni -176 marotabaga ko'paytirish.

$$x=\frac{0±\sqrt{704}}{2}$$

704 ning kvadrat ildizini chiqarish.

$$x=\frac{0±8\sqrt{11}}{2}$$

x=\frac{0±8\sqrt{11}}{2} tenglamasini yeching, bunda ± musbat.

$$x=4\sqrt{11}$$

x=\frac{0±8\sqrt{11}}{2} tenglamasini yeching, bunda ± manfiy.

$$x=-4\sqrt{11}$$

Tenglama yechildi.

$$x=4\sqrt{11} x=-4\sqrt{11}$$