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76. If the sum of three numbers in A.P., is 24 and their product is 440, find the numbers.

0 2 Views | Posted 4 months ago
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    Answered by

    Payal Gupta | Contributor-Level 10

    4 months ago

    76. Let the three numbers a − d, a, a + d be in A.P.

    Then, (a−d)+a+(a+d)=24

    ⇒ 3a = 24

    ⇒ a = 8

    and, (a−d)×a×(a+d)=440

    ⇒(a−d)(a2+ad)=440

    ⇒a3+a2d−a2d−ad2=440

    ⇒a3−ad2=440.

    ⇒a(a2−d2)=440

    Put, a=8,⇒8(a2−d2)=440

    ⇒64−d2=4408

    ⇒64−d2=55

    d2=64−55

    ⇒d2=9

    ⇒d=±3

    When d = 3, a = 8 the three number are.

    8 − 3, 8, 8 + 3 5,8,11

    When d = − 3, a = 8 the three numbers are.

    8−(−3),8,8+(−3)⇒8+3,8,8−3⇒11,8,5

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