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find the value of x if the geometric mean of 2x and 19x-2 is 7x-2

Sagot :

Shinalcantaraidn
since the geometric mean is 7x-2 then we can say that the sequence with 3 terms would be:
2x, 7x-2, 19x-2
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for it to be considered as a geometric sequence, it should have a common ratio. In which case we define the equation to find x as
(19x-2)/(7x-2) = (7x-2)/2x
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cross multiply
(19x-2)(2x) = (7x-2)(7x-2)
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distribute
38x^2-4x = 49x^2-14x-14x+4
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simplify
38x^2-4x = 49x^2-14x-14x+4
49x^2-14x-14x+4-38x^2+4x=0
11x^2-24x+4 = 0
factor
(11x-2)(x-2)=0
11x-2=0
11x=2
x=2/11
and
x-2=0
x=2
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therefore the values of 'x' would be 2/11 and 2