Solve the equation $\sqrt[3]{2 x \sqrt{x \sqrt{2 x}}} = 2$

Created: 4 months ago | Updated: 1 week ago

Job Solution Modhumoti Bank Ltd Modhumoti Bank Ltd. || Probationary Officer (2019) || 2019 গণিত

$\sqrt[3]{2 x \sqrt{x \sqrt{2 x}}} = 2$

$\Rightarrow \sqrt{2 x \sqrt{x \sqrt{2 x}}} = 2^{3} [C u b e b o t h s i d e]$

$\Rightarrow x \sqrt{x \sqrt{2 x}} = \frac{8}{2} = 4 \Rightarrow {(x \sqrt{x \sqrt{2 x}})}^{2} = 4^{2} \Rightarrow x \times x^{2} \times \sqrt{2 x} = 16$

$\Rightarrow x^{3} \times \sqrt{2 x} = 16 \Rightarrow {(x^{3} \sqrt{2 x})}^{2} = 16^{2} \Rightarrow x^{6} \times 2 \times x = 16 \times 16$

$\Rightarrow x^{7} = \frac{16 \times 16}{2} = 128 \Rightarrow x^{7} = 2^{7} ∴ x = 2$

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