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Reducing Equations to Simpler Form

Solve the fol...

Question

Solve the following equation:
$\frac{3 (x - 2) + 4 \sqrt{2 x^{3} - 3 x + 1}}{2 (x^{3} - 1)} = 1$

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Solution

$⟹ 4 \sqrt{(2 x^{3} - 3 x + 1)} = 2 x^{3} - 3 x + 4$
squaring on both sides
$32 x^{3} - 48 x + 16 = 4 x^{6} - 12 x^{4} + 16 x^{3} - 9 x^{2} - 24 x + 16$
$⟹ 4 x^{6} - 12 x^{4} - 16 x^{3} - 9 x^{2} + 24 x = 0$
$⟹ x = 0$ is one of the solution

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Reducing Equations to Simpler Form

Standard VIII Mathematics

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