64*6=25*15(x^2+1) eching

$$64 \times 6 = 25 \times 15 ( x ^ { 2 } + 1 )$$

x uchun yechish

$$x=\frac{\sqrt{15}}{25}\approx 0,154919334$$

$$x=-\frac{\sqrt{15}}{25}\approx -0,154919334$$

Kvadrat ildizini topish bo'yicha qadamlar

384 hosil qilish uchun 64 va 6 ni ko'paytirish.

$$384=25\times 15\left(x^{2}+1\right)$$

375 hosil qilish uchun 25 va 15 ni ko'paytirish.

$$384=375\left(x^{2}+1\right)$$

375 ga x^{2}+1 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$384=375x^{2}+375$$

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$375x^{2}+375=384$$

Ikkala tarafdan 375 ni ayirish.

$$375x^{2}=384-375$$

9 olish uchun 384 dan 375 ni ayirish.

$$375x^{2}=9$$

Ikki tarafini 375 ga bo‘ling.

$$x^{2}=\frac{9}{375}$$

\frac{9}{375} ulushini 3 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$x^{2}=\frac{3}{125}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$x=\frac{\sqrt{15}}{25} x=-\frac{\sqrt{15}}{25}$$

Kvadrat tenglamalaridan foydalanish qoidalari

384 hosil qilish uchun 64 va 6 ni ko'paytirish.

$$384=25\times 15\left(x^{2}+1\right)$$

375 hosil qilish uchun 25 va 15 ni ko'paytirish.

$$384=375\left(x^{2}+1\right)$$

375 ga x^{2}+1 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$384=375x^{2}+375$$

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$375x^{2}+375=384$$

Ikkala tarafdan 384 ni ayirish.

$$375x^{2}+375-384=0$$

-9 olish uchun 375 dan 384 ni ayirish.

$$375x^{2}-9=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 375 ni a, 0 ni b va -9 ni c bilan almashtiring.

$$x=\frac{0±\sqrt{0^{2}-4\times 375\left(-9\right)}}{2\times 375}$$

0 kvadratini chiqarish.

$$x=\frac{0±\sqrt{-4\times 375\left(-9\right)}}{2\times 375}$$

-4 ni 375 marotabaga ko'paytirish.

$$x=\frac{0±\sqrt{-1500\left(-9\right)}}{2\times 375}$$

-1500 ni -9 marotabaga ko'paytirish.

$$x=\frac{0±\sqrt{13500}}{2\times 375}$$

13500 ning kvadrat ildizini chiqarish.

$$x=\frac{0±30\sqrt{15}}{2\times 375}$$

2 ni 375 marotabaga ko'paytirish.

$$x=\frac{0±30\sqrt{15}}{750}$$

x=\frac{0±30\sqrt{15}}{750} tenglamasini yeching, bunda ± musbat.

$$x=\frac{\sqrt{15}}{25}$$

x=\frac{0±30\sqrt{15}}{750} tenglamasini yeching, bunda ± manfiy.

$$x=-\frac{\sqrt{15}}{25}$$

Tenglama yechildi.

$$x=\frac{\sqrt{15}}{25} x=-\frac{\sqrt{15}}{25}$$