7^2+x^2=13^2 eching

$${ 7 }^{ 2 } + { x }^{ 2 } = { 13 }^{ 2 }$$

x uchun yechish

$$x=2\sqrt{30}\approx 10,95445115$$

$$x=-2\sqrt{30}\approx -10,95445115$$

Kvadrat ildizini topish bo'yicha qadamlar

2 daraja ko‘rsatkichini 7 ga hisoblang va 49 ni qiymatni oling.

$$49+x^{2}=13^{2}$$

2 daraja ko‘rsatkichini 13 ga hisoblang va 169 ni qiymatni oling.

$$49+x^{2}=169$$

Ikkala tarafdan 49 ni ayirish.

$$x^{2}=169-49$$

120 olish uchun 169 dan 49 ni ayirish.

$$x^{2}=120$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$x=2\sqrt{30} x=-2\sqrt{30}$$

Kvadrat tenglamalaridan foydalanish qoidalari

2 daraja ko‘rsatkichini 7 ga hisoblang va 49 ni qiymatni oling.

$$49+x^{2}=13^{2}$$

2 daraja ko‘rsatkichini 13 ga hisoblang va 169 ni qiymatni oling.

$$49+x^{2}=169$$

Ikkala tarafdan 169 ni ayirish.

$$49+x^{2}-169=0$$

-120 olish uchun 49 dan 169 ni ayirish.

$$-120+x^{2}=0$$

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.

$$x^{2}-120=0$$

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 -120 ni c bilan almashtiring.

$$x=\frac{0±\sqrt{0^{2}-4\left(-120\right)}}{2}$$

0 kvadratini chiqarish.

$$x=\frac{0±\sqrt{-4\left(-120\right)}}{2}$$

-4 ni -120 marotabaga ko'paytirish.

$$x=\frac{0±\sqrt{480}}{2}$$

480 ning kvadrat ildizini chiqarish.

$$x=\frac{0±4\sqrt{30}}{2}$$

x=\frac{0±4\sqrt{30}}{2} tenglamasini yeching, bunda ± musbat.

$$x=2\sqrt{30}$$

x=\frac{0±4\sqrt{30}}{2} tenglamasini yeching, bunda ± manfiy.

$$x=-2\sqrt{30}$$

Tenglama yechildi.

$$x=2\sqrt{30} x=-2\sqrt{30}$$