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koli123able

  • 3 years ago

The sum of four numbers in A.P is 20. The ratio of the product of the first and the last numbers and the product of 2nd & 3rd numbers is 2:3 ; Find the numbers . . . ANSWER = 2,4,6,8 OR 8,6,4,2

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  1. koli123able
    • 3 years ago
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    Cant understand how to start

  2. sauravshakya
    • 3 years ago
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    Let four numbers in AP be a-3d ,a-d ,a+d and a+3d

  3. sauravshakya
    • 3 years ago
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    Now, a-3d+a-d+a+d+a+3d=20 4a=20 a=5

  4. sauravshakya
    • 3 years ago
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    Also, (a-3d)(a+3d)/ {(a-d) (a+d)} =2/3

  5. koli123able
    • 3 years ago
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    i cant understand this sentence "The ratio of the product of the first and the last numbers and the product of 2nd & 3rd numbers is 2:3"

  6. sauravshakya
    • 3 years ago
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    It simply means (a-3d)(a+3d)/ {(a-d) (a+d)} =2/3

  7. koli123able
    • 3 years ago
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    oh

  8. koli123able
    • 3 years ago
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    what should i do next.. cross multiply?

  9. sauravshakya
    • 3 years ago
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    Now, 3(a-3d)(a+3d) =2(a-d)(a+d) 3a^2 -27d^2 =2a^2 -2d^2 a^2 =25d^2 Also a=5 5^2 =25d^2 d^2=1 d=+-1

  10. sauravshakya
    • 3 years ago
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    Now, can u?

  11. koli123able
    • 3 years ago
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    ok

  12. koli123able
    • 3 years ago
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    i have to substitute the values of a and d in the four numbers which were a-3d, and so on

  13. sauravshakya
    • 3 years ago
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    yep

  14. koli123able
    • 3 years ago
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    ok got the numbers :)

  15. koli123able
    • 3 years ago
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    thanks

  16. sauravshakya
    • 3 years ago
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    welcome

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