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මේ ගාණ හදපල්ල
- Thread starter AnuradhaRa
- Start date
AL කාලේ කරේ.. දැන් මතක නෑ
මමාත් හැදුවේ මෙහෙම.. හැබැයි ඉදිරිපත් කරන විදිහ මෙහෙමද කියලා sure නෑ..
- Assumptions:
- a > b > d > 0
- Cross-multiplication:
- (a - d) / (b - d) > a / b
- (a - d)(b - d) > a(b - d)
- Expanding:
- ab - ad - bd > ab - ad
- -bd > -ad
- Dividing by the negative sign:
- bd < ad
- Dividing both sides by bd:
- 1 < a / b
- Conclusion:
- (a - d) / (b - d) > a / b
Ok, lets try,
First, let's prove the left side of the inequality,
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
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.
First, let's prove the left side of the inequality,
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
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.
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කොහොමද බං උඹලට මේව කල්පනාවට එන්නෙ. මාර හැදිල්ලක් හදල තියෙන්නෙ
මම දැං තමා බලල බලල මේක තේරුම් ගත්තෙ
@McGayan
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