(x/2^3)^2-x(3x)+15(x/2)^2=x^2 eching

$$( \frac { x } { 2 ^ { 3 } } ) ^ { 2 } - x ( 3 x ) + 15 ( \frac { x } { 2 } ) ^ { 2 } = x ^ { 2 }$$

x uchun yechish

$$x=0$$

Kvadrat ildizini topish bo'yicha qadamlar

x^{2} hosil qilish uchun x va x ni ko'paytirish.

$$\left(\frac{x}{2^{3}}\right)^{2}-x^{2}\times 3+15\times \left(\frac{x}{2}\right)^{2}=x^{2}$$

3 daraja ko‘rsatkichini 2 ga hisoblang va 8 ni qiymatni oling.

$$\left(\frac{x}{8}\right)^{2}-x^{2}\times 3+15\times \left(\frac{x}{2}\right)^{2}=x^{2}$$

\frac{x}{8}ni darajaga oshirish uchun, surat va maxrajni darajaga oshirib, keyin bo‘ling.

$$\frac{x^{2}}{8^{2}}-x^{2}\times 3+15\times \left(\frac{x}{2}\right)^{2}=x^{2}$$

Ifodalarni qo‘shish yoki ayirish uchun ularni yoyib, maxrajlarini bir xil qiling. x^{2}\times 3 ni \frac{8^{2}}{8^{2}} marotabaga ko'paytirish.

$$\frac{x^{2}}{8^{2}}-\frac{x^{2}\times 3\times 8^{2}}{8^{2}}+15\times \left(\frac{x}{2}\right)^{2}=x^{2}$$

\frac{x^{2}}{8^{2}} va \frac{x^{2}\times 3\times 8^{2}}{8^{2}} da bir xil maxraji bor, ularning suratini ayirish orqali ayiring.

$$\frac{x^{2}-x^{2}\times 3\times 8^{2}}{8^{2}}+15\times \left(\frac{x}{2}\right)^{2}=x^{2}$$

x^{2}-x^{2}\times 3\times 8^{2} ichidagi ko‘paytirishlarni bajaring.

$$\frac{x^{2}-192x^{2}}{8^{2}}+15\times \left(\frac{x}{2}\right)^{2}=x^{2}$$

x^{2}-192x^{2} kabi iboralarga o‘xshab birlashtiring.

$$\frac{-191x^{2}}{8^{2}}+15\times \left(\frac{x}{2}\right)^{2}=x^{2}$$

\frac{x}{2}ni darajaga oshirish uchun, surat va maxrajni darajaga oshirib, keyin bo‘ling.

$$\frac{-191x^{2}}{8^{2}}+15\times \frac{x^{2}}{2^{2}}=x^{2}$$

15\times \frac{x^{2}}{2^{2}} ni yagona kasrga aylantiring.

$$\frac{-191x^{2}}{8^{2}}+\frac{15x^{2}}{2^{2}}=x^{2}$$

Ifodalarni qo‘shish yoki ayirish uchun ularni yoyib, maxrajlarini bir xil qiling. 8^{2} va 2^{2} ning eng kichik umumiy karralisi 64. \frac{15x^{2}}{2^{2}} ni \frac{16}{16} marotabaga ko'paytirish.

$$\frac{-191x^{2}}{64}+\frac{16\times 15x^{2}}{64}=x^{2}$$

\frac{-191x^{2}}{64} va \frac{16\times 15x^{2}}{64} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

$$\frac{-191x^{2}+16\times 15x^{2}}{64}=x^{2}$$

-191x^{2}+16\times 15x^{2} ichidagi ko‘paytirishlarni bajaring.

$$\frac{-191x^{2}+240x^{2}}{64}=x^{2}$$

-191x^{2}+240x^{2} kabi iboralarga o‘xshab birlashtiring.

$$\frac{49x^{2}}{64}=x^{2}$$

Ikkala tarafdan x^{2} ni ayirish.

$$\frac{49x^{2}}{64}-x^{2}=0$$

Tenglamaning ikkala tarafini 64 ga ko'paytirish.

$$49x^{2}-64x^{2}=0$$

-15x^{2} ni olish uchun 49x^{2} va -64x^{2} ni birlashtirish.

$$-15x^{2}=0$$

Ikki tarafini -15 ga bo‘ling. Nol bo‘lmagan har qanday sonni nolga ko‘paytirsangiz, nol bo‘ladi.

$$x^{2}=0$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$x=0 x=0$$

Tenglama yechildi. Yechimlar bir xil.

$$x=0$$

Kvadrat tenglamalaridan foydalanish qoidalari

x^{2} hosil qilish uchun x va x ni ko'paytirish.

$$\left(\frac{x}{2^{3}}\right)^{2}-x^{2}\times 3+15\times \left(\frac{x}{2}\right)^{2}=x^{2}$$

3 daraja ko‘rsatkichini 2 ga hisoblang va 8 ni qiymatni oling.

$$\left(\frac{x}{8}\right)^{2}-x^{2}\times 3+15\times \left(\frac{x}{2}\right)^{2}=x^{2}$$

\frac{x}{8}ni darajaga oshirish uchun, surat va maxrajni darajaga oshirib, keyin bo‘ling.

$$\frac{x^{2}}{8^{2}}-x^{2}\times 3+15\times \left(\frac{x}{2}\right)^{2}=x^{2}$$

Ifodalarni qo‘shish yoki ayirish uchun ularni yoyib, maxrajlarini bir xil qiling. x^{2}\times 3 ni \frac{8^{2}}{8^{2}} marotabaga ko'paytirish.

$$\frac{x^{2}}{8^{2}}-\frac{x^{2}\times 3\times 8^{2}}{8^{2}}+15\times \left(\frac{x}{2}\right)^{2}=x^{2}$$

\frac{x^{2}}{8^{2}} va \frac{x^{2}\times 3\times 8^{2}}{8^{2}} da bir xil maxraji bor, ularning suratini ayirish orqali ayiring.

$$\frac{x^{2}-x^{2}\times 3\times 8^{2}}{8^{2}}+15\times \left(\frac{x}{2}\right)^{2}=x^{2}$$

x^{2}-x^{2}\times 3\times 8^{2} ichidagi ko‘paytirishlarni bajaring.

$$\frac{x^{2}-192x^{2}}{8^{2}}+15\times \left(\frac{x}{2}\right)^{2}=x^{2}$$

x^{2}-192x^{2} kabi iboralarga o‘xshab birlashtiring.

$$\frac{-191x^{2}}{8^{2}}+15\times \left(\frac{x}{2}\right)^{2}=x^{2}$$

\frac{x}{2}ni darajaga oshirish uchun, surat va maxrajni darajaga oshirib, keyin bo‘ling.

$$\frac{-191x^{2}}{8^{2}}+15\times \frac{x^{2}}{2^{2}}=x^{2}$$

15\times \frac{x^{2}}{2^{2}} ni yagona kasrga aylantiring.

$$\frac{-191x^{2}}{8^{2}}+\frac{15x^{2}}{2^{2}}=x^{2}$$

Ifodalarni qo‘shish yoki ayirish uchun ularni yoyib, maxrajlarini bir xil qiling. 8^{2} va 2^{2} ning eng kichik umumiy karralisi 64. \frac{15x^{2}}{2^{2}} ni \frac{16}{16} marotabaga ko'paytirish.

$$\frac{-191x^{2}}{64}+\frac{16\times 15x^{2}}{64}=x^{2}$$

\frac{-191x^{2}}{64} va \frac{16\times 15x^{2}}{64} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

$$\frac{-191x^{2}+16\times 15x^{2}}{64}=x^{2}$$

-191x^{2}+16\times 15x^{2} ichidagi ko‘paytirishlarni bajaring.

$$\frac{-191x^{2}+240x^{2}}{64}=x^{2}$$

-191x^{2}+240x^{2} kabi iboralarga o‘xshab birlashtiring.

$$\frac{49x^{2}}{64}=x^{2}$$

Ikkala tarafdan x^{2} ni ayirish.

$$\frac{49x^{2}}{64}-x^{2}=0$$

Tenglamaning ikkala tarafini 64 ga ko'paytirish.

$$49x^{2}-64x^{2}=0$$

-15x^{2} ni olish uchun 49x^{2} va -64x^{2} ni birlashtirish.

$$-15x^{2}=0$$

Ikki tarafini -15 ga bo‘ling. Nol bo‘lmagan har qanday sonni nolga ko‘paytirsangiz, nol bo‘ladi.

$$x^{2}=0$$

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 0 ni c bilan almashtiring.

$$x=\frac{0±\sqrt{0^{2}}}{2}$$

0^{2} ning kvadrat ildizini chiqarish.

$$x=\frac{0±0}{2}$$

0 ni 2 ga bo'lish.

$$x=0$$