Question

Find three rational numbers between

1. -1 and -2 2. -3/2 and 5/3 3. 5/7 and 6/7​

Answer 1

Answer:

0.1 and 0.11

57and67

14and15

Solution

Let y =-1 and x = -2

Here, x>y and we have to find three ratonal numbers, so n=3

d=y−xn+1=−1+23+1=14

Since, the three, rational numbers x and y are x+ d, x+2d and x+ 3d

now , x=d=−2+14=−8+14=−74

x+2d=−2+24=−8+24=−64=−32

and x+3d=2−34=−8+34=−54

Hene, three rational numbers between -1 and -2 are −74,−32and−54

Alternate method

let x=-1 and y =-2

we know, a rational number between x and y =x+y2

A rational number between -1 and -2 =−1−22=−32

and a rational number between -1 and −32=−1−322=−2−34=54

Similarly, −74 is a rational number between - 1and -2

Hence, required solution =32,−54,−74

(ii) let x= 0.1 and y= 0.11

Here, x<y and we have to find three rational numbers, so consider, n=3

d=y−xn+1=0.11−0.13+1=0.014

Since, the three rational numbers between x and y are (x + d) , ( x + 2d) and ( x+ 3d)

now, x+d=0.01+0.014=0.4+0.014=0.414=0.414=0.1025

x+2d=0.1+0.024=0.4+0.024=0.424=0.105

andx+3d=0.1+0.034=0.4+0.034=0.434=0.1075

Hence , three rational numbers between, 0.1 and 0.11 and 0.1025, 0.105, 0.1075

Also, without using above formula the three rational numbers between 0.1 and 0.11 are 0.101, 0.102, 0.103.

(iii) Let , x=57andy=67

Here, x<y Here, we have to find three rational numbers.

consider,

n=3,

d=y−xn+1

d=67−574=174=128

Since, the three rational number between x and y are ( x+d) , (x+2d) and (x+3d)

now, x+d=57+128=20+128=2128

x+2d=57+228=20+228=2228

x+3d=57=328=20+328=2328

Hence, three rational numbers between 57and67are2128,2228,2328

Also, without using formula, the three rational numbers between 57and67are5170,5270,5370

Let x=15andy14

Here, x<y

Here, we have to find three rational numbers.

consider, , n=3

d=y−xn+1=14−153+1=5−4204=180 since, the three rational numbers between x and y are x+d , x+2d adn x+3d.

nowx+d=15+180=16+180=1780

x+2d=15+280=16+280=1880=940

x+3d=15+380=16+380=1980

Answer 2

Step-by-step explanation:

1980 is the answer I hope it help you good night