9^2=45^2+x^2 eching

$${ 9 }^{ 2 } = { 45 }^{ 2 } + { x }^{ 2 }$$

x uchun yechish (complex solution)

$$x=-18\sqrt{6}i\approx -0-44,09081537i$$

$$x=18\sqrt{6}i\approx 44,09081537i$$

Kvadrat ildizini topish bo'yicha qadamlar

2 daraja ko‘rsatkichini 9 ga hisoblang va 81 ni qiymatni oling.

$$81=45^{2}+x^{2}$$

2 daraja ko‘rsatkichini 45 ga hisoblang va 2025 ni qiymatni oling.

$$81=2025+x^{2}$$

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$2025+x^{2}=81$$

Ikkala tarafdan 2025 ni ayirish.

$$x^{2}=81-2025$$

-1944 olish uchun 81 dan 2025 ni ayirish.

$$x^{2}=-1944$$

Tenglama yechildi.

$$x=18\sqrt{6}i x=-18\sqrt{6}i$$

Kvadrat tenglamalaridan foydalanish qoidalari

2 daraja ko‘rsatkichini 9 ga hisoblang va 81 ni qiymatni oling.

$$81=45^{2}+x^{2}$$

2 daraja ko‘rsatkichini 45 ga hisoblang va 2025 ni qiymatni oling.

$$81=2025+x^{2}$$

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$2025+x^{2}=81$$

Ikkala tarafdan 81 ni ayirish.

$$2025+x^{2}-81=0$$

1944 olish uchun 2025 dan 81 ni ayirish.

$$1944+x^{2}=0$$

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.

$$x^{2}+1944=0$$

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 1944 ni c bilan almashtiring.

$$x=\frac{0±\sqrt{0^{2}-4\times 1944}}{2}$$

0 kvadratini chiqarish.

$$x=\frac{0±\sqrt{-4\times 1944}}{2}$$

-4 ni 1944 marotabaga ko'paytirish.

$$x=\frac{0±\sqrt{-7776}}{2}$$

-7776 ning kvadrat ildizini chiqarish.

$$x=\frac{0±36\sqrt{6}i}{2}$$

x=\frac{0±36\sqrt{6}i}{2} tenglamasini yeching, bunda ± musbat.

$$x=18\sqrt{6}i$$

x=\frac{0±36\sqrt{6}i}{2} tenglamasini yeching, bunda ± manfiy.

$$x=-18\sqrt{6}i$$

Tenglama yechildi.

$$x=18\sqrt{6}i x=-18\sqrt{6}i$$