4pi-x^2pi=95 eching

$$4 \pi - x ^ { 2 } \pi = 95$$

x uchun yechish (complex solution)

$$x=-i\sqrt{\frac{95}{\pi }-4}\approx -0-5,12244465i$$

$$x=i\sqrt{\frac{95}{\pi }-4}\approx 5,12244465i$$

Kvadrat ildizini topish bo'yicha qadamlar

Ikkala tarafdan 4\pi ni ayirish.

$$-x^{2}\pi =95-4\pi$$

-\pi ga bo'lish -\pi ga ko'paytirishni bekor qiladi.

$$x^{2}=\frac{95-4\pi }{-\pi }$$

95-4\pi ni -\pi ga bo'lish.

$$x^{2}=-\frac{95}{\pi }+4$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$x=\frac{i\sqrt{95-4\pi }}{\sqrt{\pi }} x=-\frac{i\sqrt{95-4\pi }}{\sqrt{\pi }}$$

Kvadrat tenglamalaridan foydalanish qoidalari

Ikkala tarafdan 95 ni ayirish.

$$4\pi -x^{2}\pi -95=0$$

Shartlarni qayta saralash.

$$-\pi x^{2}+4\pi -95=0$$

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.

$$\left(-\pi \right)x^{2}+4\pi -95=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} -\pi ni a, 0 ni b va 4\pi -95 ni c bilan almashtiring.

$$x=\frac{0±\sqrt{0^{2}-4\left(-\pi \right)\left(4\pi -95\right)}}{2\left(-\pi \right)}$$

0 kvadratini chiqarish.

$$x=\frac{0±\sqrt{-4\left(-\pi \right)\left(4\pi -95\right)}}{2\left(-\pi \right)}$$

-4 ni -\pi marotabaga ko'paytirish.

$$x=\frac{0±\sqrt{4\pi \left(4\pi -95\right)}}{2\left(-\pi \right)}$$

4\pi \left(4\pi -95\right) ning kvadrat ildizini chiqarish.

$$x=\frac{0±2i\sqrt{\pi \left(95-4\pi \right)}}{2\left(-\pi \right)}$$

2 ni -\pi marotabaga ko'paytirish.

$$x=\frac{0±2i\sqrt{\pi \left(95-4\pi \right)}}{-2\pi }$$

x=\frac{0±2i\sqrt{\pi \left(95-4\pi \right)}}{-2\pi } tenglamasini yeching, bunda ± musbat.

$$x=-\frac{i\sqrt{95-4\pi }}{\sqrt{\pi }}$$

x=\frac{0±2i\sqrt{\pi \left(95-4\pi \right)}}{-2\pi } tenglamasini yeching, bunda ± manfiy.

$$x=\frac{i\sqrt{95-4\pi }}{\sqrt{\pi }}$$

Tenglama yechildi.

$$x=-\frac{i\sqrt{95-4\pi }}{\sqrt{\pi }} x=\frac{i\sqrt{95-4\pi }}{\sqrt{\pi }}$$