1/x=-x+25 eching

$$\frac{ 1 }{ x } = -x+25$$

x uchun yechish

$$x = \frac{3 \sqrt{69} + 25}{2} \approx 24,959935794$$

$$x=\frac{25-3\sqrt{69}}{2}\approx 0,040064206$$

Kvadrat tenglamalaridan foydalanish qoidalari

x qiymati 0 teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. Tenglamaning ikkala tarafini x ga ko'paytirish.

$$1=-xx+x\times 25$$

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

$$1=-x^{2}+x\times 25$$

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$-x^{2}+x\times 25=1$$

Ikkala tarafdan 1 ni ayirish.

$$-x^{2}+x\times 25-1=0$$

ax^{2}+bx+c=0 shaklidagi barcha tenglamalarni kvadrat formulasi bilan yechish mumkin: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. Kvadrat formula ikki yechmni taqdim qiladi, biri ± qo'shish bo'lganda, va ikkinchisi ayiruv bo'lganda.

$$-x^{2}+25x-1=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} -1 ni a, 25 ni b va -1 ni c bilan almashtiring.

$$x=\frac{-25±\sqrt{25^{2}-4\left(-1\right)\left(-1\right)}}{2\left(-1\right)}$$

25 kvadratini chiqarish.

$$x=\frac{-25±\sqrt{625-4\left(-1\right)\left(-1\right)}}{2\left(-1\right)}$$

-4 ni -1 marotabaga ko'paytirish.

$$x=\frac{-25±\sqrt{625+4\left(-1\right)}}{2\left(-1\right)}$$

4 ni -1 marotabaga ko'paytirish.

$$x=\frac{-25±\sqrt{625-4}}{2\left(-1\right)}$$

625 ni -4 ga qo'shish.

$$x=\frac{-25±\sqrt{621}}{2\left(-1\right)}$$

621 ning kvadrat ildizini chiqarish.

$$x=\frac{-25±3\sqrt{69}}{2\left(-1\right)}$$

2 ni -1 marotabaga ko'paytirish.

$$x=\frac{-25±3\sqrt{69}}{-2}$$

x=\frac{-25±3\sqrt{69}}{-2} tenglamasini yeching, bunda ± musbat. -25 ni 3\sqrt{69} ga qo'shish.

$$x=\frac{3\sqrt{69}-25}{-2}$$

-25+3\sqrt{69} ni -2 ga bo'lish.

$$x=\frac{25-3\sqrt{69}}{2}$$

x=\frac{-25±3\sqrt{69}}{-2} tenglamasini yeching, bunda ± manfiy. -25 dan 3\sqrt{69} ni ayirish.

$$x=\frac{-3\sqrt{69}-25}{-2}$$

-25-3\sqrt{69} ni -2 ga bo'lish.

$$x=\frac{3\sqrt{69}+25}{2}$$

Tenglama yechildi.

$$x=\frac{25-3\sqrt{69}}{2} x=\frac{3\sqrt{69}+25}{2}$$

Kvadratni yakunlash bo'yicha qadamlar

x qiymati 0 teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. Tenglamaning ikkala tarafini x ga ko'paytirish.

$$1=-xx+x\times 25$$

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

$$1=-x^{2}+x\times 25$$

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$-x^{2}+x\times 25=1$$

Bu kabi kvadrat tenglamalarni kvadratni yakunlab yechish mumkin. Kvadratni yechish uchun tenglama avval ushbu shaklda bo'lishi shart: x^{2}+bx=c.

$$-x^{2}+25x=1$$

Ikki tarafini -1 ga bo‘ling.

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

-1 ga bo'lish -1 ga ko'paytirishni bekor qiladi.

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

25 ni -1 ga bo'lish.

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

1 ni -1 ga bo'lish.

$$x^{2}-25x=-1$$

-25 ni bo‘lish, x shartining koeffitsienti, 2 ga -\frac{25}{2} olish uchun. Keyin, -\frac{25}{2} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

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

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib -\frac{25}{2} kvadratini chiqarish.

$$x^{2}-25x+\frac{625}{4}=-1+\frac{625}{4}$$

-1 ni \frac{625}{4} ga qo'shish.

$$x^{2}-25x+\frac{625}{4}=\frac{621}{4}$$

x^{2}-25x+\frac{625}{4} omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x-\frac{25}{2}\right)^{2}=\frac{621}{4}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-\frac{25}{2}\right)^{2}}=\sqrt{\frac{621}{4}}$$

Qisqartirish.

$$x-\frac{25}{2}=\frac{3\sqrt{69}}{2} x-\frac{25}{2}=-\frac{3\sqrt{69}}{2}$$

\frac{25}{2} ni tenglamaning ikkala tarafiga qo'shish.

$$x=\frac{3\sqrt{69}+25}{2} x=\frac{25-3\sqrt{69}}{2}$$