Réitigh sqrt{2x-3}=6^2x*sqrt{4}

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

Réitigh do x. (complex solution)

$$x=\frac{1+\sqrt{15551}i}{5184}\approx 0.000192901+0.024055488i$$

Céimeanna Réitigh

Cearnaigh an dá thaobh den chothromóid.

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

Ríomh cumhacht \sqrt{2x-3} de 2 agus faigh 2x-3.

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

Ríomh cumhacht 6 de 2 agus faigh 36.

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

Áirigh fréamh chearnach 4 agus faigh 2.

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

Méadaigh 36 agus 2 chun 72 a fháil.

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

Fairsingigh \left(72x\right)^{2}

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

Ríomh cumhacht 72 de 2 agus faigh 5184.

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

Bain 5184x^{2} ón dá thaobh.

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

Is féidir gach cothromóid san fhoirm ax^{2}+bx+c=0 a réiteach ag baint úsáid as an bhfoirmle chearnach : \frac{-b±\sqrt{b^{2}-4ac}}{2a}. Tugann an fhoirmle chearnach dhá réiteach, ceann amháin nuair is suimiú é ± agus ceann eile nuair is dealú é.

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

Tá an chothromóid seo i bhfoirm chaighdeánach: ax^{2}+bx+c=0. Cuir -5184 in ionad a, 2 in ionad b, agus -3 in ionad c san fhoirmle chearnach, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

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

Cearnóg 2.

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

Méadaigh -4 faoi -5184.

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

Méadaigh 20736 faoi -3.

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

Suimigh 4 le -62208?

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

Tóg fréamh chearnach -62204.

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

Méadaigh 2 faoi -5184.

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

Réitigh an chothromóid x=\frac{-2±2\sqrt{15551}i}{-10368} nuair is ionann ± agus plus. Suimigh -2 le 2i\sqrt{15551}?

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

Roinn -2+2i\sqrt{15551} faoi -10368.

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

Réitigh an chothromóid x=\frac{-2±2\sqrt{15551}i}{-10368} nuair is ionann ± agus míneas. Dealaigh 2i\sqrt{15551} ó -2.

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

Roinn -2-2i\sqrt{15551} faoi -10368.

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

Tá an chothromóid réitithe anois.

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

Cuir \frac{-\sqrt{15551}i+1}{5184} in ionad x sa chothromóid \sqrt{2x-3}=6^{2}x\sqrt{4}.

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

Simpligh. An chothromóid comhlíonann an luach x=\frac{-\sqrt{15551}i+1}{5184}.

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

Cuir \frac{1+\sqrt{15551}i}{5184} in ionad x sa chothromóid \sqrt{2x-3}=6^{2}x\sqrt{4}.

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

Simpligh. An luach x=\frac{1+\sqrt{15551}i}{5184} shásaíonn an gcothromóid.

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

Ag an chothromóid \sqrt{2x-3}=36\sqrt{4}x réiteach uathúil.

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