105^2=(9x)^2+(32x)^2 eching

$$105 ^ { 2 } = ( 9 x ) ^ { 2 } + ( 32 x ) ^ { 2 }$$

x uchun yechish

$$x = \frac{21 \sqrt{1105}}{221} \approx 3,158698397$$

$$x = -\frac{21 \sqrt{1105}}{221} \approx -3,158698397$$

Kvadrat ildizini topish bo'yicha qadamlar

2 daraja ko‘rsatkichini 105 ga hisoblang va 11025 ni qiymatni oling.

$$11025=\left(9x\right)^{2}+\left(32x\right)^{2}$$

\left(9x\right)^{2} ni kengaytirish.

$$11025=9^{2}x^{2}+\left(32x\right)^{2}$$

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

$$11025=81x^{2}+\left(32x\right)^{2}$$

\left(32x\right)^{2} ni kengaytirish.

$$11025=81x^{2}+32^{2}x^{2}$$

2 daraja ko‘rsatkichini 32 ga hisoblang va 1024 ni qiymatni oling.

$$11025=81x^{2}+1024x^{2}$$

1105x^{2} ni olish uchun 81x^{2} va 1024x^{2} ni birlashtirish.

$$11025=1105x^{2}$$

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$1105x^{2}=11025$$

Ikki tarafini 1105 ga bo‘ling.

$$x^{2}=\frac{11025}{1105}$$

\frac{11025}{1105} ulushini 5 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$x^{2}=\frac{2205}{221}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$x=\frac{21\sqrt{1105}}{221} x=-\frac{21\sqrt{1105}}{221}$$

Kvadrat tenglamalaridan foydalanish qoidalari

2 daraja ko‘rsatkichini 105 ga hisoblang va 11025 ni qiymatni oling.

$$11025=\left(9x\right)^{2}+\left(32x\right)^{2}$$

\left(9x\right)^{2} ni kengaytirish.

$$11025=9^{2}x^{2}+\left(32x\right)^{2}$$

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

$$11025=81x^{2}+\left(32x\right)^{2}$$

\left(32x\right)^{2} ni kengaytirish.

$$11025=81x^{2}+32^{2}x^{2}$$

2 daraja ko‘rsatkichini 32 ga hisoblang va 1024 ni qiymatni oling.

$$11025=81x^{2}+1024x^{2}$$

1105x^{2} ni olish uchun 81x^{2} va 1024x^{2} ni birlashtirish.

$$11025=1105x^{2}$$

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$1105x^{2}=11025$$

Ikkala tarafdan 11025 ni ayirish.

$$1105x^{2}-11025=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 1105 ni a, 0 ni b va -11025 ni c bilan almashtiring.

$$x=\frac{0±\sqrt{0^{2}-4\times 1105\left(-11025\right)}}{2\times 1105}$$

0 kvadratini chiqarish.

$$x=\frac{0±\sqrt{-4\times 1105\left(-11025\right)}}{2\times 1105}$$

-4 ni 1105 marotabaga ko'paytirish.

$$x=\frac{0±\sqrt{-4420\left(-11025\right)}}{2\times 1105}$$

-4420 ni -11025 marotabaga ko'paytirish.

$$x=\frac{0±\sqrt{48730500}}{2\times 1105}$$

48730500 ning kvadrat ildizini chiqarish.

$$x=\frac{0±210\sqrt{1105}}{2\times 1105}$$

2 ni 1105 marotabaga ko'paytirish.

$$x=\frac{0±210\sqrt{1105}}{2210}$$

x=\frac{0±210\sqrt{1105}}{2210} tenglamasini yeching, bunda ± musbat.

$$x=\frac{21\sqrt{1105}}{221}$$

x=\frac{0±210\sqrt{1105}}{2210} tenglamasini yeching, bunda ± manfiy.

$$x=-\frac{21\sqrt{1105}}{221}$$

Tenglama yechildi.

$$x=\frac{21\sqrt{1105}}{221} x=-\frac{21\sqrt{1105}}{221}$$