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7. The sum of four numbers in A.P. is 4 and theirproduct is 385. Find the numbers. |
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Answer» a-3d, a-d, a+d, a+3d are 4 terms in an AP(a-3d) + (a-d) + (a+d) + (a+3d) = 4 a - 3d + a - d + a - d + a + 3d = 44a = 4a=1(a-3d)(a-d)(a+3d)(a+d) = 385(a^2 - 3d^2)(a^2 - d^2 ) = 385Using a =1 ( 1 - 3d^2) ( 1 - d^2 ) = 3851 - d^2 - 3d^2 + 3d^4 = 3853d^4 - 4d^2 - 384 = 0 3d^4 - 3d^2- d^2- 384Factorise 9d⁴-10d²-385and we get d=8/3 |
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