35^2+x^2=41^2 eching

$${ 35 }^{ 2 } + { x }^{ 2 } = { 41 }^{ 2 }$$

x uchun yechish

$$x=2\sqrt{114}\approx 21,354156504$$

$$x=-2\sqrt{114}\approx -21,354156504$$

Kvadrat ildizini topish bo'yicha qadamlar

2 daraja ko‘rsatkichini 35 ga hisoblang va 1225 ni qiymatni oling.

$$1225+x^{2}=41^{2}$$

2 daraja ko‘rsatkichini 41 ga hisoblang va 1681 ni qiymatni oling.

$$1225+x^{2}=1681$$

Ikkala tarafdan 1225 ni ayirish.

$$x^{2}=1681-1225$$

456 olish uchun 1681 dan 1225 ni ayirish.

$$x^{2}=456$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$x=2\sqrt{114} x=-2\sqrt{114}$$

Kvadrat tenglamalaridan foydalanish qoidalari

2 daraja ko‘rsatkichini 35 ga hisoblang va 1225 ni qiymatni oling.

$$1225+x^{2}=41^{2}$$

2 daraja ko‘rsatkichini 41 ga hisoblang va 1681 ni qiymatni oling.

$$1225+x^{2}=1681$$

Ikkala tarafdan 1681 ni ayirish.

$$1225+x^{2}-1681=0$$

-456 olish uchun 1225 dan 1681 ni ayirish.

$$-456+x^{2}=0$$

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.

$$x^{2}-456=0$$

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 -456 ni c bilan almashtiring.

$$x=\frac{0±\sqrt{0^{2}-4\left(-456\right)}}{2}$$

0 kvadratini chiqarish.

$$x=\frac{0±\sqrt{-4\left(-456\right)}}{2}$$

-4 ni -456 marotabaga ko'paytirish.

$$x=\frac{0±\sqrt{1824}}{2}$$

1824 ning kvadrat ildizini chiqarish.

$$x=\frac{0±4\sqrt{114}}{2}$$

x=\frac{0±4\sqrt{114}}{2} tenglamasini yeching, bunda ± musbat.

$$x=2\sqrt{114}$$

x=\frac{0±4\sqrt{114}}{2} tenglamasini yeching, bunda ± manfiy.

$$x=-2\sqrt{114}$$

Tenglama yechildi.

$$x=2\sqrt{114} x=-2\sqrt{114}$$