Question

insert x arithmetic mean between x^2 and 1.need genuine, correct answers, since it's important, incorrect answers will be reported immediately..... V. V important..​

Answer 1

Answer:

Let A1, A2, ...., Ax be the x arithmetic means between 1 and x². Then,

1, A1, A2, ...., Ax, x² is an A.P.

Let d be the common difference of this A.P. Clealry, it contains (x + 2) terms.

Therefore, x² = (x + 2)th term

x² = 1 + (x + 1)d

d = x²-1/x+1

d = x-1

Now,

A1 = a + d = a + (x - 1)

A2 = a + 2d = a + 2(x - 1)

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.

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Ax = a + xd = a + x(x - 1)

These are the required arithmetic means between 1 and x2