Question

3(2 to the power x +1)-2 to the power x + to the power 2 + 5=0​

Answer 1

One of ways that I can think of is to change the fractions to same denominator and then dividing it by 2(that is finding mean of two numbers).

Let me show it to you:

To find the first rational number between 1/2 and 1/5 = 1/2(1/2 + 1/5) = 1/2(7/10) = 7/20

Clearly, 1/2>7/20>1/51/2>7/20>1/5

Now to find the second rational number,take either 1/2 , 7/20 at a time or 7/20 , 1/5 .

Let me demonstrate both methods:

Taking 1/2 , 7/20 together:

Rational number between 1/2,7/20= 1/2(1/2 + 7/20)=1/2(34/40)=1/2(17/20)= 17/40 Now 1/2>17/40>7/20>1/5

Taking 7/20 ,1/5 together:

Rational number between 7/20,1/5=1/2(7/20 + 1/5)= 1/2(55/100)=1/2(11/20)=11/40 Now 1/2>7/20>11/40>1/5

Hope it helps!