{left(16*x/10right)}^2+x^2=4318^2 eching

$${ \left( \frac{ 16 \times x }{ 10 } \right) }^{ 2 } + { x }^{ 2 } = { 4318 }^{ 2 }$$

x uchun yechish

$$x = \frac{21590 \sqrt{89}}{89} \approx 2288,535422934$$

$$x = -\frac{21590 \sqrt{89}}{89} \approx -2288,535422934$$

Kvadrat ildizini topish bo'yicha qadamlar

\frac{8}{5}x ni olish uchun 16x ni 10 ga bo‘ling.

$$\left(\frac{8}{5}x\right)^{2}+x^{2}=4318^{2}$$

\left(\frac{8}{5}x\right)^{2} ni kengaytirish.

$$\left(\frac{8}{5}\right)^{2}x^{2}+x^{2}=4318^{2}$$

2 daraja ko‘rsatkichini \frac{8}{5} ga hisoblang va \frac{64}{25} ni qiymatni oling.

$$\frac{64}{25}x^{2}+x^{2}=4318^{2}$$

\frac{89}{25}x^{2} ni olish uchun \frac{64}{25}x^{2} va x^{2} ni birlashtirish.

$$\frac{89}{25}x^{2}=4318^{2}$$

2 daraja ko‘rsatkichini 4318 ga hisoblang va 18645124 ni qiymatni oling.

$$\frac{89}{25}x^{2}=18645124$$

Ikki tarafini \frac{25}{89} va teskari kasri \frac{89}{25} ga ko‘paytiring.

$$x^{2}=18645124\times \frac{25}{89}$$

\frac{466128100}{89} hosil qilish uchun 18645124 va \frac{25}{89} ni ko'paytirish.

$$x^{2}=\frac{466128100}{89}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$x=\frac{21590\sqrt{89}}{89} x=-\frac{21590\sqrt{89}}{89}$$

Kvadrat tenglamalaridan foydalanish qoidalari

\frac{8}{5}x ni olish uchun 16x ni 10 ga bo‘ling.

$$\left(\frac{8}{5}x\right)^{2}+x^{2}=4318^{2}$$

\left(\frac{8}{5}x\right)^{2} ni kengaytirish.

$$\left(\frac{8}{5}\right)^{2}x^{2}+x^{2}=4318^{2}$$

2 daraja ko‘rsatkichini \frac{8}{5} ga hisoblang va \frac{64}{25} ni qiymatni oling.

$$\frac{64}{25}x^{2}+x^{2}=4318^{2}$$

\frac{89}{25}x^{2} ni olish uchun \frac{64}{25}x^{2} va x^{2} ni birlashtirish.

$$\frac{89}{25}x^{2}=4318^{2}$$

2 daraja ko‘rsatkichini 4318 ga hisoblang va 18645124 ni qiymatni oling.

$$\frac{89}{25}x^{2}=18645124$$

Ikkala tarafdan 18645124 ni ayirish.

$$\frac{89}{25}x^{2}-18645124=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} \frac{89}{25} ni a, 0 ni b va -18645124 ni c bilan almashtiring.

$$x=\frac{0±\sqrt{0^{2}-4\times \frac{89}{25}\left(-18645124\right)}}{2\times \frac{89}{25}}$$

0 kvadratini chiqarish.

$$x=\frac{0±\sqrt{-4\times \frac{89}{25}\left(-18645124\right)}}{2\times \frac{89}{25}}$$

-4 ni \frac{89}{25} marotabaga ko'paytirish.

$$x=\frac{0±\sqrt{-\frac{356}{25}\left(-18645124\right)}}{2\times \frac{89}{25}}$$

-\frac{356}{25} ni -18645124 marotabaga ko'paytirish.

$$x=\frac{0±\sqrt{\frac{6637664144}{25}}}{2\times \frac{89}{25}}$$

\frac{6637664144}{25} ning kvadrat ildizini chiqarish.

$$x=\frac{0±\frac{8636\sqrt{89}}{5}}{2\times \frac{89}{25}}$$

2 ni \frac{89}{25} marotabaga ko'paytirish.

$$x=\frac{0±\frac{8636\sqrt{89}}{5}}{\frac{178}{25}}$$

x=\frac{0±\frac{8636\sqrt{89}}{5}}{\frac{178}{25}} tenglamasini yeching, bunda ± musbat.

$$x=\frac{21590\sqrt{89}}{89}$$

x=\frac{0±\frac{8636\sqrt{89}}{5}}{\frac{178}{25}} tenglamasini yeching, bunda ± manfiy.

$$x=-\frac{21590\sqrt{89}}{89}$$

Tenglama yechildi.

$$x=\frac{21590\sqrt{89}}{89} x=-\frac{21590\sqrt{89}}{89}$$