39424/100*7/22=r^2 eching

$$\frac { 39424 } { 100 } \times \frac { 7 } { 22 } = r ^ { 2 }$$

r uchun yechish

$$r = \frac{56}{5} = 11\frac{1}{5} = 11,2$$

$$r = -\frac{56}{5} = -11\frac{1}{5} = -11,2$$

Kvadratlar farqidan foydalangan qadamlar

\frac{39424}{100} ulushini 4 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$\frac{9856}{25}\times \frac{7}{22}=r^{2}$$

\frac{3136}{25} hosil qilish uchun \frac{9856}{25} va \frac{7}{22} ni ko'paytirish.

$$\frac{3136}{25}=r^{2}$$

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$r^{2}=\frac{3136}{25}$$

Ikkala tarafdan \frac{3136}{25} ni ayirish.

$$r^{2}-\frac{3136}{25}=0$$

Ikkala tarafini 25 ga ko‘paytiring.

$$25r^{2}-3136=0$$

Hisoblang: 25r^{2}-3136. 25r^{2}-3136 ni \left(5r\right)^{2}-56^{2} sifatida qaytadan yozish. Kvadratlarning farqini ushbu formula bilan hisoblash mumkin: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(5r-56\right)\left(5r+56\right)=0$$

Tenglamani yechish uchun 5r-56=0 va 5r+56=0 ni yeching.

$$r=\frac{56}{5} r=-\frac{56}{5}$$

Kvadrat ildizini topish bo'yicha qadamlar

\frac{39424}{100} ulushini 4 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$\frac{9856}{25}\times \frac{7}{22}=r^{2}$$

\frac{3136}{25} hosil qilish uchun \frac{9856}{25} va \frac{7}{22} ni ko'paytirish.

$$\frac{3136}{25}=r^{2}$$

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$r^{2}=\frac{3136}{25}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$r=\frac{56}{5} r=-\frac{56}{5}$$

Kvadrat tenglamalaridan foydalanish qoidalari

\frac{39424}{100} ulushini 4 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$\frac{9856}{25}\times \frac{7}{22}=r^{2}$$

\frac{3136}{25} hosil qilish uchun \frac{9856}{25} va \frac{7}{22} ni ko'paytirish.

$$\frac{3136}{25}=r^{2}$$

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$r^{2}=\frac{3136}{25}$$

Ikkala tarafdan \frac{3136}{25} ni ayirish.

$$r^{2}-\frac{3136}{25}=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 1 ni a, 0 ni b va -\frac{3136}{25} ni c bilan almashtiring.

$$r=\frac{0±\sqrt{0^{2}-4\left(-\frac{3136}{25}\right)}}{2}$$

0 kvadratini chiqarish.

$$r=\frac{0±\sqrt{-4\left(-\frac{3136}{25}\right)}}{2}$$

-4 ni -\frac{3136}{25} marotabaga ko'paytirish.

$$r=\frac{0±\sqrt{\frac{12544}{25}}}{2}$$

\frac{12544}{25} ning kvadrat ildizini chiqarish.

$$r=\frac{0±\frac{112}{5}}{2}$$

r=\frac{0±\frac{112}{5}}{2} tenglamasini yeching, bunda ± musbat.

$$r=\frac{56}{5}$$

r=\frac{0±\frac{112}{5}}{2} tenglamasini yeching, bunda ± manfiy.

$$r=-\frac{56}{5}$$

Tenglama yechildi.

$$r=\frac{56}{5} r=-\frac{56}{5}$$