x^2=2y/y eching

$$x ^ { 2 } = \frac { 2 y } { y }$$

x uchun yechish (complex solution)

$$x=-\sqrt{2}\approx -1,414213562$$

$$x=\sqrt{2}\approx 1,414213562\text{, }y\neq 0$$

Kvadrat ildizini topish bo'yicha qadamlar

Tenglama yechildi.

$$x=\sqrt{2} x=-\sqrt{2}$$

Kvadrat tenglamalaridan foydalanish qoidalari

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.

$$x^{2}=2$$

Tenglamaning ikkala tarafidan 2 ni ayirish.

$$x^{2}-2=2-2$$

O‘zidan 2 ayirilsa 0 qoladi.

$$x^{2}-2=0$$

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 -2 ni c bilan almashtiring.

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

0 kvadratini chiqarish.

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

-4 ni -2 marotabaga ko'paytirish.

$$x=\frac{0±\sqrt{8}}{2}$$

8 ning kvadrat ildizini chiqarish.

$$x=\frac{0±2\sqrt{2}}{2}$$

x=\frac{0±2\sqrt{2}}{2} tenglamasini yeching, bunda ± musbat.

$$x=\sqrt{2}$$

x=\frac{0±2\sqrt{2}}{2} tenglamasini yeching, bunda ± manfiy.

$$x=-\sqrt{2}$$

Tenglama yechildi.

$$x=\sqrt{2} x=-\sqrt{2}$$

y uchun yechish (complex solution)

$$y\neq 0$$

$$\left(x=-\sqrt{2}\text{ or }x=\sqrt{2}\right)\text{ and }y\neq 0$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

y qiymati 0 teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. Tenglamaning ikkala tarafini y ga ko'paytirish.

$$yx^{2}=2y$$

Ikkala tarafdan 2y ni ayirish.

$$yx^{2}-2y=0$$

y'ga ega bo'lgan barcha shartlarni birlashtirish.

$$\left(x^{2}-2\right)y=0$$

0 ni x^{2}-2 ga bo'lish.

$$y=0$$

y qiymati 0 teng bo‘lmaydi.

$$y\in \emptyset$$

y uchun yechish

$$y\neq 0$$

$$|x|=\sqrt{2}\text{ and }y\neq 0$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

y qiymati 0 teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. Tenglamaning ikkala tarafini y ga ko'paytirish.

$$yx^{2}=2y$$

Ikkala tarafdan 2y ni ayirish.

$$yx^{2}-2y=0$$

y'ga ega bo'lgan barcha shartlarni birlashtirish.

$$\left(x^{2}-2\right)y=0$$

0 ni x^{2}-2 ga bo'lish.

$$y=0$$

y qiymati 0 teng bo‘lmaydi.

$$y\in \emptyset$$

x uchun yechish

$$x=\sqrt{2}$$

$$x=-\sqrt{2}\text{, }y\neq 0$$