lambda^2-4999001lambda/100000+0000225=0 eching

$$\lambda ^ { 2 } - \frac { 4999001 \lambda } { 100000 } + 0000225 = 0$$

λ uchun yechish

$$\lambda =\frac{4999001}{100000}=49,99001$$

$$\lambda =0$$

Faktorlash qadamlari

Tenglamaning ikkala tarafini 100000 ga ko'paytirish.

$$100000\lambda ^{2}-4999001\lambda +0\times 0\times 0\times 0\times 225=0$$

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

$$100000\lambda ^{2}-4999001\lambda +0\times 0\times 0\times 225=0$$

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

$$100000\lambda ^{2}-4999001\lambda +0\times 0\times 225=0$$

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

$$100000\lambda ^{2}-4999001\lambda +0\times 225=0$$

0 hosil qilish uchun 0 va 225 ni ko'paytirish.

$$100000\lambda ^{2}-4999001\lambda +0=0$$

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

$$100000\lambda ^{2}-4999001\lambda =0$$

\lambda omili.

$$\lambda \left(100000\lambda -4999001\right)=0$$

Tenglamani yechish uchun \lambda =0 va 100000\lambda -4999001=0 ni yeching.

$$\lambda =0 \lambda =\frac{4999001}{100000}$$

Kvadrat tenglamalaridan foydalanish qoidalari

Tenglamaning ikkala tarafini 100000 ga ko'paytirish.

$$100000\lambda ^{2}-4999001\lambda +0\times 0\times 0\times 0\times 225=0$$

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

$$100000\lambda ^{2}-4999001\lambda +0\times 0\times 0\times 225=0$$

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

$$100000\lambda ^{2}-4999001\lambda +0\times 0\times 225=0$$

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

$$100000\lambda ^{2}-4999001\lambda +0\times 225=0$$

0 hosil qilish uchun 0 va 225 ni ko'paytirish.

$$100000\lambda ^{2}-4999001\lambda +0=0$$

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

$$100000\lambda ^{2}-4999001\lambda =0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 100000 ni a, -4999001 ni b va 0 ni c bilan almashtiring.

$$\lambda =\frac{-\left(-4999001\right)±\sqrt{\left(-4999001\right)^{2}}}{2\times 100000}$$

\left(-4999001\right)^{2} ning kvadrat ildizini chiqarish.

$$\lambda =\frac{-\left(-4999001\right)±4999001}{2\times 100000}$$

-4999001 ning teskarisi 4999001 ga teng.

$$\lambda =\frac{4999001±4999001}{2\times 100000}$$

2 ni 100000 marotabaga ko'paytirish.

$$\lambda =\frac{4999001±4999001}{200000}$$

\lambda =\frac{4999001±4999001}{200000} tenglamasini yeching, bunda ± musbat. 4999001 ni 4999001 ga qo'shish.

$$\lambda =\frac{9998002}{200000}$$

\frac{9998002}{200000} ulushini 2 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$\lambda =\frac{4999001}{100000}$$

\lambda =\frac{4999001±4999001}{200000} tenglamasini yeching, bunda ± manfiy. 4999001 dan 4999001 ni ayirish.

$$\lambda =\frac{0}{200000}$$

0 ni 200000 ga bo'lish.

$$\lambda =0$$

Tenglama yechildi.

$$\lambda =\frac{4999001}{100000} \lambda =0$$

Kvadratni yakunlash bo'yicha qadamlar

Tenglamaning ikkala tarafini 100000 ga ko'paytirish.

$$100000\lambda ^{2}-4999001\lambda +0\times 0\times 0\times 0\times 225=0$$

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

$$100000\lambda ^{2}-4999001\lambda +0\times 0\times 0\times 225=0$$

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

$$100000\lambda ^{2}-4999001\lambda +0\times 0\times 225=0$$

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

$$100000\lambda ^{2}-4999001\lambda +0\times 225=0$$

0 hosil qilish uchun 0 va 225 ni ko'paytirish.

$$100000\lambda ^{2}-4999001\lambda +0=0$$

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

$$100000\lambda ^{2}-4999001\lambda =0$$

Ikki tarafini 100000 ga bo‘ling.

$$\frac{100000\lambda ^{2}-4999001\lambda }{100000}=\frac{0}{100000}$$

100000 ga bo'lish 100000 ga ko'paytirishni bekor qiladi.

$$\lambda ^{2}-\frac{4999001}{100000}\lambda =\frac{0}{100000}$$

0 ni 100000 ga bo'lish.

$$\lambda ^{2}-\frac{4999001}{100000}\lambda =0$$

-\frac{4999001}{100000} ni bo‘lish, x shartining koeffitsienti, 2 ga -\frac{4999001}{200000} olish uchun. Keyin, -\frac{4999001}{200000} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$\lambda ^{2}-\frac{4999001}{100000}\lambda +\left(-\frac{4999001}{200000}\right)^{2}=\left(-\frac{4999001}{200000}\right)^{2}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib -\frac{4999001}{200000} kvadratini chiqarish.

$$\lambda ^{2}-\frac{4999001}{100000}\lambda +\frac{24990010998001}{40000000000}=\frac{24990010998001}{40000000000}$$

\lambda ^{2}-\frac{4999001}{100000}\lambda +\frac{24990010998001}{40000000000} omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(\lambda -\frac{4999001}{200000}\right)^{2}=\frac{24990010998001}{40000000000}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(\lambda -\frac{4999001}{200000}\right)^{2}}=\sqrt{\frac{24990010998001}{40000000000}}$$

Qisqartirish.

$$\lambda -\frac{4999001}{200000}=\frac{4999001}{200000} \lambda -\frac{4999001}{200000}=-\frac{4999001}{200000}$$

\frac{4999001}{200000} ni tenglamaning ikkala tarafiga qo'shish.

$$\lambda =\frac{4999001}{100000} \lambda =0$$