16y^2=24y-09 eching

$$16 { y }^{ 2 } = 24y-09$$

y uchun yechish

$$y = \frac{3}{2} = 1\frac{1}{2} = 1,5$$

$$y=0$$

Faktorlash qadamlari

0 hosil qilish uchun 0 va 9 ni ko'paytirish.

$$16y^{2}=24y-0$$

0 ni ikki tarafga qo’shing.

$$16y^{2}+0=24y$$

Har qanday songa nolni qo‘shsangiz, o‘zi chiqadi.

$$16y^{2}=24y$$

Ikkala tarafdan 24y ni ayirish.

$$16y^{2}-24y=0$$

y omili.

$$y\left(16y-24\right)=0$$

Tenglamani yechish uchun y=0 va 16y-24=0 ni yeching.

$$y=0 y=\frac{3}{2}$$

Kvadrat tenglamalaridan foydalanish qoidalari

0 hosil qilish uchun 0 va 9 ni ko'paytirish.

$$16y^{2}=24y-0$$

0 ni ikki tarafga qo’shing.

$$16y^{2}+0=24y$$

Har qanday songa nolni qo‘shsangiz, o‘zi chiqadi.

$$16y^{2}=24y$$

Ikkala tarafdan 24y ni ayirish.

$$16y^{2}-24y=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 16 ni a, -24 ni b va 0 ni c bilan almashtiring.

$$y=\frac{-\left(-24\right)±\sqrt{\left(-24\right)^{2}}}{2\times 16}$$

\left(-24\right)^{2} ning kvadrat ildizini chiqarish.

$$y=\frac{-\left(-24\right)±24}{2\times 16}$$

-24 ning teskarisi 24 ga teng.

$$y=\frac{24±24}{2\times 16}$$

2 ni 16 marotabaga ko'paytirish.

$$y=\frac{24±24}{32}$$

y=\frac{24±24}{32} tenglamasini yeching, bunda ± musbat. 24 ni 24 ga qo'shish.

$$y=\frac{48}{32}$$

\frac{48}{32} ulushini 16 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$y=\frac{3}{2}$$

y=\frac{24±24}{32} tenglamasini yeching, bunda ± manfiy. 24 dan 24 ni ayirish.

$$y=\frac{0}{32}$$

0 ni 32 ga bo'lish.

$$y=0$$

Tenglama yechildi.

$$y=\frac{3}{2} y=0$$

Kvadratni yakunlash bo'yicha qadamlar

0 hosil qilish uchun 0 va 9 ni ko'paytirish.

$$16y^{2}=24y-0$$

Ikkala tarafdan 24y ni ayirish.

$$16y^{2}-24y=-0$$

0 hosil qilish uchun -1 va 0 ni ko'paytirish.

$$16y^{2}-24y=0$$

Ikki tarafini 16 ga bo‘ling.

$$\frac{16y^{2}-24y}{16}=\frac{0}{16}$$

16 ga bo'lish 16 ga ko'paytirishni bekor qiladi.

$$y^{2}+\left(-\frac{24}{16}\right)y=\frac{0}{16}$$

\frac{-24}{16} ulushini 8 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$y^{2}-\frac{3}{2}y=\frac{0}{16}$$

0 ni 16 ga bo'lish.

$$y^{2}-\frac{3}{2}y=0$$

-\frac{3}{2} ni bo‘lish, x shartining koeffitsienti, 2 ga -\frac{3}{4} olish uchun. Keyin, -\frac{3}{4} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$y^{2}-\frac{3}{2}y+\left(-\frac{3}{4}\right)^{2}=\left(-\frac{3}{4}\right)^{2}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib -\frac{3}{4} kvadratini chiqarish.

$$y^{2}-\frac{3}{2}y+\frac{9}{16}=\frac{9}{16}$$

y^{2}-\frac{3}{2}y+\frac{9}{16} omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(y-\frac{3}{4}\right)^{2}=\frac{9}{16}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(y-\frac{3}{4}\right)^{2}}=\sqrt{\frac{9}{16}}$$

Qisqartirish.

$$y-\frac{3}{4}=\frac{3}{4} y-\frac{3}{4}=-\frac{3}{4}$$

\frac{3}{4} ni tenglamaning ikkala tarafiga qo'shish.

$$y=\frac{3}{2} y=0$$