5/4x^2-1/2x+025-65^2=0 eching

$$\frac{ 5 }{ 4 } { x }^{ 2 } - \frac{ 1 }{ 2 } x+025- { 65 }^{ 2 } =0$$

x uchun yechish

$$x = \frac{3 \sqrt{9389} + 1}{5} \approx 58,338111424$$

$$x=\frac{1-3\sqrt{9389}}{5}\approx -57,938111424$$

Kvadrat tenglamalaridan foydalanish qoidalari

0 hosil qilish uchun 0 va 25 ni ko'paytirish.

$$\frac{5}{4}x^{2}-\frac{1}{2}x+0-65^{2}=0$$

Har qanday songa nolni qo‘shsangiz, o‘zi chiqadi.

$$\frac{5}{4}x^{2}-\frac{1}{2}x-65^{2}=0$$

2 daraja ko‘rsatkichini 65 ga hisoblang va 4225 ni qiymatni oling.

$$\frac{5}{4}x^{2}-\frac{1}{2}x-4225=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} \frac{5}{4} ni a, -\frac{1}{2} ni b va -4225 ni c bilan almashtiring.

$$x=\frac{-\left(-\frac{1}{2}\right)±\sqrt{\left(-\frac{1}{2}\right)^{2}-4\times \frac{5}{4}\left(-4225\right)}}{2\times \frac{5}{4}}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib -\frac{1}{2} kvadratini chiqarish.

$$x=\frac{-\left(-\frac{1}{2}\right)±\sqrt{\frac{1}{4}-4\times \frac{5}{4}\left(-4225\right)}}{2\times \frac{5}{4}}$$

-4 ni \frac{5}{4} marotabaga ko'paytirish.

$$x=\frac{-\left(-\frac{1}{2}\right)±\sqrt{\frac{1}{4}-5\left(-4225\right)}}{2\times \frac{5}{4}}$$

-5 ni -4225 marotabaga ko'paytirish.

$$x=\frac{-\left(-\frac{1}{2}\right)±\sqrt{\frac{1}{4}+21125}}{2\times \frac{5}{4}}$$

\frac{1}{4} ni 21125 ga qo'shish.

$$x=\frac{-\left(-\frac{1}{2}\right)±\sqrt{\frac{84501}{4}}}{2\times \frac{5}{4}}$$

\frac{84501}{4} ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-\frac{1}{2}\right)±\frac{3\sqrt{9389}}{2}}{2\times \frac{5}{4}}$$

-\frac{1}{2} ning teskarisi \frac{1}{2} ga teng.

$$x=\frac{\frac{1}{2}±\frac{3\sqrt{9389}}{2}}{2\times \frac{5}{4}}$$

2 ni \frac{5}{4} marotabaga ko'paytirish.

$$x=\frac{\frac{1}{2}±\frac{3\sqrt{9389}}{2}}{\frac{5}{2}}$$

x=\frac{\frac{1}{2}±\frac{3\sqrt{9389}}{2}}{\frac{5}{2}} tenglamasini yeching, bunda ± musbat. \frac{1}{2} ni \frac{3\sqrt{9389}}{2} ga qo'shish.

$$x=\frac{3\sqrt{9389}+1}{2\times \frac{5}{2}}$$

\frac{1+3\sqrt{9389}}{2} ni \frac{5}{2} ga bo'lish \frac{1+3\sqrt{9389}}{2} ga k'paytirish \frac{5}{2} ga qaytarish.

$$x=\frac{3\sqrt{9389}+1}{5}$$

x=\frac{\frac{1}{2}±\frac{3\sqrt{9389}}{2}}{\frac{5}{2}} tenglamasini yeching, bunda ± manfiy. \frac{1}{2} dan \frac{3\sqrt{9389}}{2} ni ayirish.

$$x=\frac{1-3\sqrt{9389}}{2\times \frac{5}{2}}$$

\frac{1-3\sqrt{9389}}{2} ni \frac{5}{2} ga bo'lish \frac{1-3\sqrt{9389}}{2} ga k'paytirish \frac{5}{2} ga qaytarish.

$$x=\frac{1-3\sqrt{9389}}{5}$$

Tenglama yechildi.

$$x=\frac{3\sqrt{9389}+1}{5} x=\frac{1-3\sqrt{9389}}{5}$$

Kvadratni yakunlash bo'yicha qadamlar

0 hosil qilish uchun 0 va 25 ni ko'paytirish.

$$\frac{5}{4}x^{2}-\frac{1}{2}x+0-65^{2}=0$$

Har qanday songa nolni qo‘shsangiz, o‘zi chiqadi.

$$\frac{5}{4}x^{2}-\frac{1}{2}x-65^{2}=0$$

2 daraja ko‘rsatkichini 65 ga hisoblang va 4225 ni qiymatni oling.

$$\frac{5}{4}x^{2}-\frac{1}{2}x-4225=0$$

4225 ni ikki tarafga qo’shing. Har qanday songa nolni qo‘shsangiz, o‘zi chiqadi.

$$\frac{5}{4}x^{2}-\frac{1}{2}x=4225$$

Tenglamaning ikki tarafini \frac{5}{4} ga bo'lish, bu kasrni qaytarish orqali ikkala tarafga ko'paytirish bilan aynidir.

$$\frac{\frac{5}{4}x^{2}-\frac{1}{2}x}{\frac{5}{4}}=\frac{4225}{\frac{5}{4}}$$

\frac{5}{4} ga bo'lish \frac{5}{4} ga ko'paytirishni bekor qiladi.

$$x^{2}+\left(-\frac{\frac{1}{2}}{\frac{5}{4}}\right)x=\frac{4225}{\frac{5}{4}}$$

-\frac{1}{2} ni \frac{5}{4} ga bo'lish -\frac{1}{2} ga k'paytirish \frac{5}{4} ga qaytarish.

$$x^{2}-\frac{2}{5}x=\frac{4225}{\frac{5}{4}}$$

4225 ni \frac{5}{4} ga bo'lish 4225 ga k'paytirish \frac{5}{4} ga qaytarish.

$$x^{2}-\frac{2}{5}x=3380$$

-\frac{2}{5} ni bo‘lish, x shartining koeffitsienti, 2 ga -\frac{1}{5} olish uchun. Keyin, -\frac{1}{5} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}-\frac{2}{5}x+\left(-\frac{1}{5}\right)^{2}=3380+\left(-\frac{1}{5}\right)^{2}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib -\frac{1}{5} kvadratini chiqarish.

$$x^{2}-\frac{2}{5}x+\frac{1}{25}=3380+\frac{1}{25}$$

3380 ni \frac{1}{25} ga qo'shish.

$$x^{2}-\frac{2}{5}x+\frac{1}{25}=\frac{84501}{25}$$

x^{2}-\frac{2}{5}x+\frac{1}{25} omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x-\frac{1}{5}\right)^{2}=\frac{84501}{25}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-\frac{1}{5}\right)^{2}}=\sqrt{\frac{84501}{25}}$$

Qisqartirish.

$$x-\frac{1}{5}=\frac{3\sqrt{9389}}{5} x-\frac{1}{5}=-\frac{3\sqrt{9389}}{5}$$

\frac{1}{5} ni tenglamaning ikkala tarafiga qo'shish.

$$x=\frac{3\sqrt{9389}+1}{5} x=\frac{1-3\sqrt{9389}}{5}$$