(3-x/2)^2+5-y/4=0 eching

$$( \frac { 3 - x } { 2 } ) ^ { 2 } + \frac { 5 - y } { 4 } = 0$$

y uchun yechish

$$y=\left(x-3\right)^{2}+5$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

Tenglamaning ikkala tarafini 4 ga ko'paytirish.

$$4\times \left(\frac{3-x}{2}\right)^{2}+5-y=0$$

\frac{3-x}{2}ni darajaga oshirish uchun, surat va maxrajni darajaga oshirib, keyin bo‘ling.

$$4\times \frac{\left(3-x\right)^{2}}{2^{2}}+5-y=0$$

4\times \frac{\left(3-x\right)^{2}}{2^{2}} ni yagona kasrga aylantiring.

$$\frac{4\left(3-x\right)^{2}}{2^{2}}+5-y=0$$

Ifodalarni qo‘shish yoki ayirish uchun ularni yoyib, maxrajlarini bir xil qiling. 5-y ni \frac{2^{2}}{2^{2}} marotabaga ko'paytirish.

$$\frac{4\left(3-x\right)^{2}}{2^{2}}+\frac{\left(5-y\right)\times 2^{2}}{2^{2}}=0$$

\frac{4\left(3-x\right)^{2}}{2^{2}} va \frac{\left(5-y\right)\times 2^{2}}{2^{2}} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

$$\frac{4\left(3-x\right)^{2}+\left(5-y\right)\times 2^{2}}{2^{2}}=0$$

4\left(3-x\right)^{2}+\left(5-y\right)\times 2^{2} ichidagi ko‘paytirishlarni bajaring.

$$\frac{36-24x+4x^{2}+20-4y}{2^{2}}=0$$

36-24x+4x^{2}+20-4y kabi iboralarga o‘xshab birlashtiring.

$$\frac{56-24x+4x^{2}-4y}{2^{2}}=0$$

2 daraja ko‘rsatkichini 2 ga hisoblang va 4 ni qiymatni oling.

$$\frac{56-24x+4x^{2}-4y}{4}=0$$

14-6x+x^{2}-y natijani olish uchun 56-24x+4x^{2}-4y ning har bir ifodasini 4 ga bo‘ling.

$$14-6x+x^{2}-y=0$$

Ikkala tarafdan 14 ni ayirish. Har qanday sonni noldan ayirsangiz, o‘zining manfiyi chiqadi.

$$-6x+x^{2}-y=-14$$

6x ni ikki tarafga qo’shing.

$$x^{2}-y=-14+6x$$

Ikkala tarafdan x^{2} ni ayirish.

$$-y=-14+6x-x^{2}$$

Tenglama standart shaklda.

$$-y=-x^{2}+6x-14$$

Ikki tarafini -1 ga bo‘ling.

$$\frac{-y}{-1}=\frac{-x^{2}+6x-14}{-1}$$

-1 ga bo'lish -1 ga ko'paytirishni bekor qiladi.

$$y=\frac{-x^{2}+6x-14}{-1}$$

-14+6x-x^{2} ni -1 ga bo'lish.

$$y=x^{2}-6x+14$$

x uchun yechish (complex solution)

$$x=\sqrt{y-5}+3$$

$$x=-\sqrt{y-5}+3$$

x uchun yechish

$$x=\sqrt{y-5}+3$$

$$x=-\sqrt{y-5}+3\text{, }y\geq 5$$