y^2-9/25-y^2/36=1 eching

$$\frac { y ^ { 2 } - 9 } { 25 } - \frac { y ^ { 2 } } { 36 } = 1$$

y uchun yechish

$$y = \frac{6 \sqrt{374}}{11} \approx 10,548588876$$

$$y = -\frac{6 \sqrt{374}}{11} \approx -10,548588876$$

Kvadrat ildizini topish bo'yicha qadamlar

Tenglamaning ikkala tarafini 900 ga, 25,36 ning eng kichik karralisiga ko‘paytiring.

$$36\left(y^{2}-9\right)-25y^{2}=900$$

36 ga y^{2}-9 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$36y^{2}-324-25y^{2}=900$$

11y^{2} ni olish uchun 36y^{2} va -25y^{2} ni birlashtirish.

$$11y^{2}-324=900$$

324 ni ikki tarafga qo’shing.

$$11y^{2}=900+324$$

1224 olish uchun 900 va 324'ni qo'shing.

$$11y^{2}=1224$$

Ikki tarafini 11 ga bo‘ling.

$$y^{2}=\frac{1224}{11}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$y=\frac{6\sqrt{374}}{11} y=-\frac{6\sqrt{374}}{11}$$

Kvadrat tenglamalaridan foydalanish qoidalari

Tenglamaning ikkala tarafini 900 ga, 25,36 ning eng kichik karralisiga ko‘paytiring.

$$36\left(y^{2}-9\right)-25y^{2}=900$$

36 ga y^{2}-9 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$36y^{2}-324-25y^{2}=900$$

11y^{2} ni olish uchun 36y^{2} va -25y^{2} ni birlashtirish.

$$11y^{2}-324=900$$

Ikkala tarafdan 900 ni ayirish.

$$11y^{2}-324-900=0$$

-1224 olish uchun -324 dan 900 ni ayirish.

$$11y^{2}-1224=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 11 ni a, 0 ni b va -1224 ni c bilan almashtiring.

$$y=\frac{0±\sqrt{0^{2}-4\times 11\left(-1224\right)}}{2\times 11}$$

0 kvadratini chiqarish.

$$y=\frac{0±\sqrt{-4\times 11\left(-1224\right)}}{2\times 11}$$

-4 ni 11 marotabaga ko'paytirish.

$$y=\frac{0±\sqrt{-44\left(-1224\right)}}{2\times 11}$$

-44 ni -1224 marotabaga ko'paytirish.

$$y=\frac{0±\sqrt{53856}}{2\times 11}$$

53856 ning kvadrat ildizini chiqarish.

$$y=\frac{0±12\sqrt{374}}{2\times 11}$$

2 ni 11 marotabaga ko'paytirish.

$$y=\frac{0±12\sqrt{374}}{22}$$

y=\frac{0±12\sqrt{374}}{22} tenglamasini yeching, bunda ± musbat.

$$y=\frac{6\sqrt{374}}{11}$$

y=\frac{0±12\sqrt{374}}{22} tenglamasini yeching, bunda ± manfiy.

$$y=-\frac{6\sqrt{374}}{11}$$

Tenglama yechildi.

$$y=\frac{6\sqrt{374}}{11} y=-\frac{6\sqrt{374}}{11}$$