68x^2=120-33sqrt{15} eching

$$68 { x }^{ 2 } =120-33 \sqrt{ 15 }$$

x uchun yechish (complex solution)

$$x=-\frac{i\sqrt{561\sqrt{15}-2040}}{34}\approx -0-0,338865981i$$

$$x=\frac{i\sqrt{561\sqrt{15}-2040}}{34}\approx 0,338865981i$$

Kvadrat ildizini topish bo'yicha qadamlar

68 ga bo'lish 68 ga ko'paytirishni bekor qiladi.

$$x^{2}=\frac{120-33\sqrt{15}}{68}$$

120-33\sqrt{15} ni 68 ga bo'lish.

$$x^{2}=-\frac{33\sqrt{15}}{68}+\frac{30}{17}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$x=\frac{i\sqrt{561\sqrt{15}-2040}}{34} x=-\frac{i\sqrt{561\sqrt{15}-2040}}{34}$$

Kvadrat tenglamalaridan foydalanish qoidalari

Ikkala tarafdan 120 ni ayirish.

$$68x^{2}-120=-33\sqrt{15}$$

33\sqrt{15} ni ikki tarafga qo’shing.

$$68x^{2}-120+33\sqrt{15}=0$$

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.

$$68x^{2}+33\sqrt{15}-120=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 68 ni a, 0 ni b va -120+33\sqrt{15} ni c bilan almashtiring.

$$x=\frac{0±\sqrt{0^{2}-4\times 68\left(33\sqrt{15}-120\right)}}{2\times 68}$$

0 kvadratini chiqarish.

$$x=\frac{0±\sqrt{-4\times 68\left(33\sqrt{15}-120\right)}}{2\times 68}$$

-4 ni 68 marotabaga ko'paytirish.

$$x=\frac{0±\sqrt{-272\left(33\sqrt{15}-120\right)}}{2\times 68}$$

-272 ni -120+33\sqrt{15} marotabaga ko'paytirish.

$$x=\frac{0±\sqrt{32640-8976\sqrt{15}}}{2\times 68}$$

32640-8976\sqrt{15} ning kvadrat ildizini chiqarish.

$$x=\frac{0±4i\sqrt{561\sqrt{15}-2040}}{2\times 68}$$

2 ni 68 marotabaga ko'paytirish.

$$x=\frac{0±4i\sqrt{561\sqrt{15}-2040}}{136}$$

x=\frac{0±4i\sqrt{561\sqrt{15}-2040}}{136} tenglamasini yeching, bunda ± musbat.

$$x=\frac{i\sqrt{561\sqrt{15}-2040}}{34}$$

x=\frac{0±4i\sqrt{561\sqrt{15}-2040}}{136} tenglamasini yeching, bunda ± manfiy.

$$x=-\frac{i\sqrt{561\sqrt{15}-2040}}{34}$$

Tenglama yechildi.

$$x=\frac{i\sqrt{561\sqrt{15}-2040}}{34} x=-\frac{i\sqrt{561\sqrt{15}-2040}}{34}$$