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प्रश्न
Divide 24 in three parts such that they are in AP and their product is 440.
उत्तर
Let the required parts of 24 be (a- d) , a and (a +d) such that they are in AP.
Then (a-d) + a+ (a +d) = 24
⇒ 3a = 24
⇒ a=8
Also , (a-d) .a. (a+d) = 440
⇒ `a(a^2 - d^2 )= 440`
⇒` 8(64 - d^2 ) = 440`
⇒`d^2 = 64 - 55 = 9`
⇒ `d= +-3`
Thus , a = 8 and d = `+-3`
Hence, the required parts of 24 are (5,8,11) or (11,8,5).
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