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Insert x arithmetic means between x^{2} and 1.

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Insert $x$ arithmetic means between $x^{2}$ and $1$ .

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Insert

x

arithmetic means between

x^{2}

and

1

12 mins ago

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Text solutionVerified

The sequence will from an A.P with

a = x^{2}

and

t_{x + 2} = 1

t_{n} = a + (n - 1) d \Rightarrow t_{x + 2} = a + (x + 2 - 1) d \Rightarrow 1 = x^{2} + (x + 1) d \Rightarrow 1 - x^{2} = (x + 1) d \Rightarrow (x + 1) (x - 1) = (x + 1) d \Rightarrow d = 1 - x

So the arithmetic means are

a + d, a + 2 d + a + 3 d ........... a + (x + 1) d \Rightarrow x^{2} - x + 1, x^{2} - 2 x + 2, ......., x

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Question Text	Insert $x$ arithmetic means between $x^{2}$ and $1$ .
Answer Type	Text solution:1
Upvotes	150