n^2-25n+72=0 eching

$$n ^ { 2 } - 25 n + 72 = 0$$

n uchun yechish

$$n = \frac{\sqrt{337} + 25}{2} \approx 21,678779875$$

$$n = \frac{25 - \sqrt{337}}{2} \approx 3,321220125$$

Kvadrat tenglamalaridan foydalanish qoidalari

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.

$$n^{2}-25n+72=0$$

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 72 ni c bilan almashtiring.

$$n=\frac{-\left(-25\right)±\sqrt{\left(-25\right)^{2}-4\times 72}}{2}$$

-25 kvadratini chiqarish.

$$n=\frac{-\left(-25\right)±\sqrt{625-4\times 72}}{2}$$

-4 ni 72 marotabaga ko'paytirish.

$$n=\frac{-\left(-25\right)±\sqrt{625-288}}{2}$$

625 ni -288 ga qo'shish.

$$n=\frac{-\left(-25\right)±\sqrt{337}}{2}$$

-25 ning teskarisi 25 ga teng.

$$n=\frac{25±\sqrt{337}}{2}$$

n=\frac{25±\sqrt{337}}{2} tenglamasini yeching, bunda ± musbat. 25 ni \sqrt{337} ga qo'shish.

$$n=\frac{\sqrt{337}+25}{2}$$

n=\frac{25±\sqrt{337}}{2} tenglamasini yeching, bunda ± manfiy. 25 dan \sqrt{337} ni ayirish.

$$n=\frac{25-\sqrt{337}}{2}$$

Tenglama yechildi.

$$n=\frac{\sqrt{337}+25}{2} n=\frac{25-\sqrt{337}}{2}$$

Kvadratni yakunlash bo'yicha qadamlar

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

$$n^{2}-25n+72=0$$

Tenglamaning ikkala tarafidan 72 ni ayirish.

$$n^{2}-25n+72-72=-72$$

O‘zidan 72 ayirilsa 0 qoladi.

$$n^{2}-25n=-72$$

-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.

$$n^{2}-25n+\left(-\frac{25}{2}\right)^{2}=-72+\left(-\frac{25}{2}\right)^{2}$$

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

$$n^{2}-25n+\frac{625}{4}=-72+\frac{625}{4}$$

-72 ni \frac{625}{4} ga qo'shish.

$$n^{2}-25n+\frac{625}{4}=\frac{337}{4}$$

n^{2}-25n+\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.

$$\left(n-\frac{25}{2}\right)^{2}=\frac{337}{4}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(n-\frac{25}{2}\right)^{2}}=\sqrt{\frac{337}{4}}$$

Qisqartirish.

$$n-\frac{25}{2}=\frac{\sqrt{337}}{2} n-\frac{25}{2}=-\frac{\sqrt{337}}{2}$$

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

$$n=\frac{\sqrt{337}+25}{2} n=\frac{25-\sqrt{337}}{2}$$