99^2+x^2=125^2 eching

$${ 99 }^{ 2 } + { x }^{ 2 } = { 125 }^{ 2 }$$

x uchun yechish

$$x=8\sqrt{91}\approx 76,315136113$$

$$x=-8\sqrt{91}\approx -76,315136113$$

Kvadrat ildizini topish bo'yicha qadamlar

2 daraja ko‘rsatkichini 99 ga hisoblang va 9801 ni qiymatni oling.

$$9801+x^{2}=125^{2}$$

2 daraja ko‘rsatkichini 125 ga hisoblang va 15625 ni qiymatni oling.

$$9801+x^{2}=15625$$

Ikkala tarafdan 9801 ni ayirish.

$$x^{2}=15625-9801$$

5824 olish uchun 15625 dan 9801 ni ayirish.

$$x^{2}=5824$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$x=8\sqrt{91} x=-8\sqrt{91}$$

Kvadrat tenglamalaridan foydalanish qoidalari

2 daraja ko‘rsatkichini 99 ga hisoblang va 9801 ni qiymatni oling.

$$9801+x^{2}=125^{2}$$

2 daraja ko‘rsatkichini 125 ga hisoblang va 15625 ni qiymatni oling.

$$9801+x^{2}=15625$$

Ikkala tarafdan 15625 ni ayirish.

$$9801+x^{2}-15625=0$$

-5824 olish uchun 9801 dan 15625 ni ayirish.

$$-5824+x^{2}=0$$

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.

$$x^{2}-5824=0$$

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 -5824 ni c bilan almashtiring.

$$x=\frac{0±\sqrt{0^{2}-4\left(-5824\right)}}{2}$$

0 kvadratini chiqarish.

$$x=\frac{0±\sqrt{-4\left(-5824\right)}}{2}$$

-4 ni -5824 marotabaga ko'paytirish.

$$x=\frac{0±\sqrt{23296}}{2}$$

23296 ning kvadrat ildizini chiqarish.

$$x=\frac{0±16\sqrt{91}}{2}$$

x=\frac{0±16\sqrt{91}}{2} tenglamasini yeching, bunda ± musbat.

$$x=8\sqrt{91}$$

x=\frac{0±16\sqrt{91}}{2} tenglamasini yeching, bunda ± manfiy.

$$x=-8\sqrt{91}$$

Tenglama yechildi.

$$x=8\sqrt{91} x=-8\sqrt{91}$$