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posysaeva2
@posysaeva2
July 2022
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Известно что 64 х^2+ 1/х^2= 65. найдите значение выражения 8x+1/x.
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Verified answer
64 х^2+ 1/х^2 =
= (8 х)^2+ (1/х)^2 =
= (8 х)^2+ 2*(8х)*(1/х) +(1/х)^2 - 2*(8х)*(1/х) =
= (8 х+ 1/х)^2 - 2*8 =
= (8 х+ 1/х)^2 - 16 =65
(8 х+ 1/х)^2 - 16 = 65
(8 х+ 1/х)^2 = 16 + 65 = 81 = 9^2 = (-9)^2
(8 х+ 1/х) =9 или -9
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Verified answer
64 х^2+ 1/х^2 == (8 х)^2+ (1/х)^2 =
= (8 х)^2+ 2*(8х)*(1/х) +(1/х)^2 - 2*(8х)*(1/х) =
= (8 х+ 1/х)^2 - 2*8 =
= (8 х+ 1/х)^2 - 16 =65(8 х+ 1/х)^2 - 16 = 65
(8 х+ 1/х)^2 = 16 + 65 = 81 = 9^2 = (-9)^2
(8 х+ 1/х) =9 или -9