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प्रश्न
Find three rational numbers between –1 and –2
उत्तर १
Let y = –1 and x = –2
Here, x > y and we have to find three rational numbers, so n = 3
∵ `d = (y - x)/(n + 1)`
= `(-1 + 2)/(3 + 1)`
= `1/4`
Since, the three rational numbers between x and y are x + d, x + 2d and x + 3d.
Now, `x + d = -2 + 1/4`
= `(-8 + 1)/4`
= `(-7)/4`
`x + 2d = -2 + 2/4`
= `(-8 + 2)/4`
= `(-6)/4`
= `(-3)/2`
And `x + 3d = - 2 + 3/4`
= `(-8 + 3)/4`
= `(-5)/4`
Hence, three rational numbers between –1 and –2 are `(-7)/4, (-3)/2` and `(-5)/4`
उत्तर २
Let x = –1 and y = –2
We know, a rational number between x and y = `(x + y)/2`
A rational number between –1 and –2
= `(-1 - 2)/2`
= `-3/2`
And a rational number between –1 and `-3/2`
= `(-1 - 3/2)/2`
= `(-2 - 3)/4`
= `-5/4`
Similarly, `-7/4` is a rational number between –1 and –2.
Hence, required solution = `-3/2, -5/4, -7/4`
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