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Solving Equations with Variables on Both Sides

Solve the fol...

Question

Solve the following equations:
$\sqrt{2 x^{2} - 7 x + 1} - \sqrt{2 x^{2} - 9 x + 4} = 1$ .

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Solution

$\sqrt{2 x^{2} - 7 x + 1} - \sqrt{2 x^{2} - 9 x + 4} = 1 \sqrt{2 x^{2} - 7 x + 1} = 1 + \sqrt{2 x^{2} - 9 x + 4}$
Squaring both sides, we get
$2 x^{2} - 7 x + 1 = 1 + 2 x^{2} - 9 x + 4 + 2 \sqrt{2 x^{2} - 9 x + 4} 2 x - 4 = 2 \sqrt{2 x^{2} - 9 x + 4} x - 2 = \sqrt{2 x^{2} - 9 x + 4}$
Again squaring both sides
${(x - 2)}^{2} = 2 x^{2} - 9 x + 4 x^{2} + 4 - 4 x = 2 x^{2} - 9 x + 4 x^{2} - 5 x = 0 x (x - 5) = 0 \Rightarrow x = 0, 5$

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Solving Equations with Variables on Both Sides

Standard VIII Mathematics

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