6^2-x^2=2*25*4 eching

$$6 ^ { 2 } - x ^ { 2 } = 2 \times 25 \times 4$$

x uchun yechish (complex solution)

$$x=-2\sqrt{41}i\approx -0-12,806248475i$$

$$x=2\sqrt{41}i\approx 12,806248475i$$

Kvadrat ildizini topish bo'yicha qadamlar

2 daraja ko‘rsatkichini 6 ga hisoblang va 36 ni qiymatni oling.

$$36-x^{2}=2\times 25\times 4$$

50 hosil qilish uchun 2 va 25 ni ko'paytirish.

$$36-x^{2}=50\times 4$$

200 hosil qilish uchun 50 va 4 ni ko'paytirish.

$$36-x^{2}=200$$

Ikkala tarafdan 36 ni ayirish.

$$-x^{2}=200-36$$

164 olish uchun 200 dan 36 ni ayirish.

$$-x^{2}=164$$

Ikki tarafini -1 ga bo‘ling.

$$x^{2}=-164$$

Tenglama yechildi.

$$x=2\sqrt{41}i x=-2\sqrt{41}i$$

Kvadrat tenglamalaridan foydalanish qoidalari

2 daraja ko‘rsatkichini 6 ga hisoblang va 36 ni qiymatni oling.

$$36-x^{2}=2\times 25\times 4$$

50 hosil qilish uchun 2 va 25 ni ko'paytirish.

$$36-x^{2}=50\times 4$$

200 hosil qilish uchun 50 va 4 ni ko'paytirish.

$$36-x^{2}=200$$

Ikkala tarafdan 200 ni ayirish.

$$36-x^{2}-200=0$$

-164 olish uchun 36 dan 200 ni ayirish.

$$-164-x^{2}=0$$

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.

$$-x^{2}-164=0$$

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 -164 ni c bilan almashtiring.

$$x=\frac{0±\sqrt{0^{2}-4\left(-1\right)\left(-164\right)}}{2\left(-1\right)}$$

0 kvadratini chiqarish.

$$x=\frac{0±\sqrt{-4\left(-1\right)\left(-164\right)}}{2\left(-1\right)}$$

-4 ni -1 marotabaga ko'paytirish.

$$x=\frac{0±\sqrt{4\left(-164\right)}}{2\left(-1\right)}$$

4 ni -164 marotabaga ko'paytirish.

$$x=\frac{0±\sqrt{-656}}{2\left(-1\right)}$$

-656 ning kvadrat ildizini chiqarish.

$$x=\frac{0±4\sqrt{41}i}{2\left(-1\right)}$$

2 ni -1 marotabaga ko'paytirish.

$$x=\frac{0±4\sqrt{41}i}{-2}$$

x=\frac{0±4\sqrt{41}i}{-2} tenglamasini yeching, bunda ± musbat.

$$x=-2\sqrt{41}i$$

x=\frac{0±4\sqrt{41}i}{-2} tenglamasini yeching, bunda ± manfiy.

$$x=2\sqrt{41}i$$

Tenglama yechildi.

$$x=-2\sqrt{41}i x=2\sqrt{41}i$$