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

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

y uchun yechish

$$y=-\frac{24\sqrt{61}i}{61}\approx -0-3,072885118i$$

$$y=\frac{24\sqrt{61}i}{61}\approx 3,072885118i$$

Kvadrat ildizini topish bo'yicha qadamlar

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

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

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

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

-61y^{2} ni olish uchun -36y^{2} va -25y^{2} ni birlashtirish.

$$324-61y^{2}=900$$

Ikkala tarafdan 324 ni ayirish.

$$-61y^{2}=900-324$$

576 olish uchun 900 dan 324 ni ayirish.

$$-61y^{2}=576$$

Ikki tarafini -61 ga bo‘ling.

$$y^{2}=-\frac{576}{61}$$

Tenglama yechildi.

$$y=\frac{24\sqrt{61}i}{61} y=-\frac{24\sqrt{61}i}{61}$$

Kvadrat tenglamalaridan foydalanish qoidalari

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

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

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

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

-61y^{2} ni olish uchun -36y^{2} va -25y^{2} ni birlashtirish.

$$324-61y^{2}=900$$

Ikkala tarafdan 900 ni ayirish.

$$324-61y^{2}-900=0$$

-576 olish uchun 324 dan 900 ni ayirish.

$$-576-61y^{2}=0$$

Bu kabi kvadrat tenglamalarni x^{2} sharti bilan, biroq x shartisiz hamon kvadrat tenglamasidan foydalanib yechish mumkin, \frac{-b±\sqrt{b^{2}-4ac}}{2a}, ular standart formulaga solingandan so'ng: ax^{2}+bx+c=0.

$$-61y^{2}-576=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} -61 ni a, 0 ni b va -576 ni c bilan almashtiring.

$$y=\frac{0±\sqrt{0^{2}-4\left(-61\right)\left(-576\right)}}{2\left(-61\right)}$$

0 kvadratini chiqarish.

$$y=\frac{0±\sqrt{-4\left(-61\right)\left(-576\right)}}{2\left(-61\right)}$$

-4 ni -61 marotabaga ko'paytirish.

$$y=\frac{0±\sqrt{244\left(-576\right)}}{2\left(-61\right)}$$

244 ni -576 marotabaga ko'paytirish.

$$y=\frac{0±\sqrt{-140544}}{2\left(-61\right)}$$

-140544 ning kvadrat ildizini chiqarish.

$$y=\frac{0±48\sqrt{61}i}{2\left(-61\right)}$$

2 ni -61 marotabaga ko'paytirish.

$$y=\frac{0±48\sqrt{61}i}{-122}$$

y=\frac{0±48\sqrt{61}i}{-122} tenglamasini yeching, bunda ± musbat.

$$y=-\frac{24\sqrt{61}i}{61}$$

y=\frac{0±48\sqrt{61}i}{-122} tenglamasini yeching, bunda ± manfiy.

$$y=\frac{24\sqrt{61}i}{61}$$

Tenglama yechildi.

$$y=-\frac{24\sqrt{61}i}{61} y=\frac{24\sqrt{61}i}{61}$$