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ElaKiri Talk!
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<blockquote data-quote="adithyag" data-source="post: 28883672" data-attributes="member: 558196"><p>Ok, lets try,</p><p></p><p>First, let's prove the left side of the inequality,</p><p></p><p>[ATTACH=full]205861[/ATTACH]</p><p></p><p>Cross-multiplying the inequality gives:</p><p></p><p>(b - d) × (a / b) > (a - d)</p><p></p><p>Expanding both sides of the inequality:</p><p></p><p>(a * b - d * b) > (a * (b - d) - d * (b - d))</p><p></p><p>Simplifying:</p><p></p><p>(a * b - d * b) > (a * b - a * d - d * b + d^2)</p><p></p><p>The b terms cancel out:</p><p></p><p>(a * b - a * d) > (a * b - a * d - d * b + d^2)</p><p></p><p>Simplifying further:</p><p></p><p>-a * d > -d * b + d^2</p><p></p><p>Dividing both sides by -d (remembering that d is positive):</p><p></p><p>a < b - d + d^2 / d</p><p></p><p>a < b - d + d</p><p></p><p>a < b</p><p></p><p>Since a > b, this inequality is not true. Therefore, the left side of the original inequality is false.</p><p></p><p></p><p>Next, let's prove the right side of the inequality</p><p></p><p>[ATTACH=full]205863[/ATTACH]</p><p></p><p>Cross-multiplying the inequality gives:</p><p></p><p>b * (a / b) > a + d</p><p></p><p>Simplifying:</p><p></p><p>a > a + d - b</p><p></p><p>-a > d - b</p><p></p><p>Since b > d, the right side of the inequality is not true. Therefore, the right side of the original inequality is false.</p><p></p><p>Since both sides of the original inequality are false, we cannot prove the given inequality using the provided conditions a > b > d > 0.</p></blockquote><p></p>
[QUOTE="adithyag, post: 28883672, member: 558196"] Ok, lets try, First, let's prove the left side of the inequality, [ATTACH type="full"]205861[/ATTACH] Cross-multiplying the inequality gives: (b - d) × (a / b) > (a - d) Expanding both sides of the inequality: (a * b - d * b) > (a * (b - d) - d * (b - d)) Simplifying: (a * b - d * b) > (a * b - a * d - d * b + d^2) The b terms cancel out: (a * b - a * d) > (a * b - a * d - d * b + d^2) Simplifying further: -a * d > -d * b + d^2 Dividing both sides by -d (remembering that d is positive): a < b - d + d^2 / d a < b - d + d a < b Since a > b, this inequality is not true. Therefore, the left side of the original inequality is false. Next, let's prove the right side of the inequality [ATTACH type="full"]205863[/ATTACH] Cross-multiplying the inequality gives: b * (a / b) > a + d Simplifying: a > a + d - b -a > d - b Since b > d, the right side of the inequality is not true. Therefore, the right side of the original inequality is false. Since both sides of the original inequality are false, we cannot prove the given inequality using the provided conditions a > b > d > 0. [/QUOTE]
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