144/169=r^2 eching

$$\frac { 144 } { 169 } = r ^ { 2 }$$

r uchun yechish

$$r=\frac{12}{13}\approx 0,923076923$$

$$r=-\frac{12}{13}\approx -0,923076923$$

Kvadratlar farqidan foydalangan qadamlar

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$r^{2}=\frac{144}{169}$$

Ikkala tarafdan \frac{144}{169} ni ayirish.

$$r^{2}-\frac{144}{169}=0$$

Ikkala tarafini 169 ga ko‘paytiring.

$$169r^{2}-144=0$$

Hisoblang: 169r^{2}-144. 169r^{2}-144 ni \left(13r\right)^{2}-12^{2} sifatida qaytadan yozish. Kvadratlarning farqini ushbu formula bilan hisoblash mumkin: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(13r-12\right)\left(13r+12\right)=0$$

Tenglamani yechish uchun 13r-12=0 va 13r+12=0 ni yeching.

$$r=\frac{12}{13} r=-\frac{12}{13}$$

Kvadrat ildizini topish bo'yicha qadamlar

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$r^{2}=\frac{144}{169}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$r=\frac{12}{13} r=-\frac{12}{13}$$

Kvadrat tenglamalaridan foydalanish qoidalari

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$r^{2}=\frac{144}{169}$$

Ikkala tarafdan \frac{144}{169} ni ayirish.

$$r^{2}-\frac{144}{169}=0$$

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{144}{169} ni c bilan almashtiring.

$$r=\frac{0±\sqrt{0^{2}-4\left(-\frac{144}{169}\right)}}{2}$$

0 kvadratini chiqarish.

$$r=\frac{0±\sqrt{-4\left(-\frac{144}{169}\right)}}{2}$$

-4 ni -\frac{144}{169} marotabaga ko'paytirish.

$$r=\frac{0±\sqrt{\frac{576}{169}}}{2}$$

\frac{576}{169} ning kvadrat ildizini chiqarish.

$$r=\frac{0±\frac{24}{13}}{2}$$

r=\frac{0±\frac{24}{13}}{2} tenglamasini yeching, bunda ± musbat.

$$r=\frac{12}{13}$$

r=\frac{0±\frac{24}{13}}{2} tenglamasini yeching, bunda ± manfiy.

$$r=-\frac{12}{13}$$

Tenglama yechildi.

$$r=\frac{12}{13} r=-\frac{12}{13}$$