sqrt{2x-3}=6^2x*sqrt{4} eching

$$\sqrt { 2 x - 3 } = 6 ^ { 2 } x \cdot \sqrt { 4 }$$

x uchun yechish (complex solution)

$$x=\frac{1+\sqrt{15551}i}{5184}\approx 0,000192901+0,024055488i$$

Yechim qadamlari

Tenglamaning ikkala taraf kvadratini chiqarish.

$$\left(\sqrt{2x-3}\right)^{2}=\left(6^{2}x\sqrt{4}\right)^{2}$$

2 daraja ko‘rsatkichini \sqrt{2x-3} ga hisoblang va 2x-3 ni qiymatni oling.

$$2x-3=\left(6^{2}x\sqrt{4}\right)^{2}$$

2 daraja ko‘rsatkichini 6 ga hisoblang va 36 ni qiymatni oling.

$$2x-3=\left(36x\sqrt{4}\right)^{2}$$

4 ning kvadrat ildizini hisoblab, 2 natijaga ega bo‘ling.

$$2x-3=\left(36x\times 2\right)^{2}$$

72 hosil qilish uchun 36 va 2 ni ko'paytirish.

$$2x-3=\left(72x\right)^{2}$$

\left(72x\right)^{2} ni kengaytirish.

$$2x-3=72^{2}x^{2}$$

2 daraja ko‘rsatkichini 72 ga hisoblang va 5184 ni qiymatni oling.

$$2x-3=5184x^{2}$$

Ikkala tarafdan 5184x^{2} ni ayirish.

$$2x-3-5184x^{2}=0$$

ax^{2}+bx+c=0 shaklidagi barcha tenglamalarni kvadrat formulasi bilan yechish mumkin: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. Kvadrat formula ikki yechmni taqdim qiladi, biri ± qo'shish bo'lganda, va ikkinchisi ayiruv bo'lganda.

$$-5184x^{2}+2x-3=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} -5184 ni a, 2 ni b va -3 ni c bilan almashtiring.

$$x=\frac{-2±\sqrt{2^{2}-4\left(-5184\right)\left(-3\right)}}{2\left(-5184\right)}$$

2 kvadratini chiqarish.

$$x=\frac{-2±\sqrt{4-4\left(-5184\right)\left(-3\right)}}{2\left(-5184\right)}$$

-4 ni -5184 marotabaga ko'paytirish.

$$x=\frac{-2±\sqrt{4+20736\left(-3\right)}}{2\left(-5184\right)}$$

20736 ni -3 marotabaga ko'paytirish.

$$x=\frac{-2±\sqrt{4-62208}}{2\left(-5184\right)}$$

4 ni -62208 ga qo'shish.

$$x=\frac{-2±\sqrt{-62204}}{2\left(-5184\right)}$$

-62204 ning kvadrat ildizini chiqarish.

$$x=\frac{-2±2\sqrt{15551}i}{2\left(-5184\right)}$$

2 ni -5184 marotabaga ko'paytirish.

$$x=\frac{-2±2\sqrt{15551}i}{-10368}$$

x=\frac{-2±2\sqrt{15551}i}{-10368} tenglamasini yeching, bunda ± musbat. -2 ni 2i\sqrt{15551} ga qo'shish.

$$x=\frac{-2+2\sqrt{15551}i}{-10368}$$

-2+2i\sqrt{15551} ni -10368 ga bo'lish.

$$x=\frac{-\sqrt{15551}i+1}{5184}$$

x=\frac{-2±2\sqrt{15551}i}{-10368} tenglamasini yeching, bunda ± manfiy. -2 dan 2i\sqrt{15551} ni ayirish.

$$x=\frac{-2\sqrt{15551}i-2}{-10368}$$

-2-2i\sqrt{15551} ni -10368 ga bo'lish.

$$x=\frac{1+\sqrt{15551}i}{5184}$$

Tenglama yechildi.

$$x=\frac{-\sqrt{15551}i+1}{5184} x=\frac{1+\sqrt{15551}i}{5184}$$

\sqrt{2x-3}=6^{2}x\sqrt{4} tenglamasida x uchun \frac{-\sqrt{15551}i+1}{5184} ni almashtiring.

$$\sqrt{2\times \frac{-\sqrt{15551}i+1}{5184}-3}=6^{2}\times \frac{-\sqrt{15551}i+1}{5184}\sqrt{4}$$

Qisqartirish. x=\frac{-\sqrt{15551}i+1}{5184} qiymati bu tenglamani qoniqtirmaydi.

$$-\left(\frac{1}{72}-\frac{1}{72}i\times 15551^{\frac{1}{2}}\right)=-\frac{1}{72}i\times 15551^{\frac{1}{2}}+\frac{1}{72}$$

\sqrt{2x-3}=6^{2}x\sqrt{4} tenglamasida x uchun \frac{1+\sqrt{15551}i}{5184} ni almashtiring.

$$\sqrt{2\times \frac{1+\sqrt{15551}i}{5184}-3}=6^{2}\times \frac{1+\sqrt{15551}i}{5184}\sqrt{4}$$

Qisqartirish. x=\frac{1+\sqrt{15551}i}{5184} tenglamani qoniqtiradi.

$$\frac{1}{72}+\frac{1}{72}i\times 15551^{\frac{1}{2}}=\frac{1}{72}+\frac{1}{72}i\times 15551^{\frac{1}{2}}$$

\sqrt{2x-3}=36\sqrt{4}x tenglamasi noyob yechimga ega.

$$x=\frac{1+\sqrt{15551}i}{5184}$$