Question

Can anyone help me with the question please​

Answer 1

Explanation:

7 a)

Step 1 :

Make the denominators the same

`-(1)/(7) \ and \ (2)/(9)`

`-(1)/(7) * (9)/(9) = -(9)/(63)\\\\(2)/(9) * (7)/(7) = (14)/(63)\\`

Step 2 :

Now find rational between (-9/63) and (14/63).

Just change the number in the numerator. Write any numbers between -9 and 14 in the numerator.

`( -8)/(63), \ (-7)/(63),\ (3)/(63),\ (6)/(63),\ (8)/(63)`

7 b )

`x = 3 + 2\sqrt2\\\\x + (1)/(x) = (3 + 2\sqrt2) + (1)/(3+2\sqrt2)`

`[ Rationalize \ the \ denominator : (1)/(3 + \sqrt2) * (3 - 2\sqrt2)/(3-2\sqrt 2) = (3 - 2 \sqrt2)/(3^2 - (2 \sqrt2)^2 ) = (3 - 2\sqrt2)/(9 - 8) = 3 - 2\sqrt 2 \ ]`

`therefore , x + (1)/(x) = 3 + 2\sqrt 2 + 3 - 2 \sqrt 2 = 6 + 0 = 6`

Answer 2

Explanation: