1.Squaring both sides,

(x^(1/4)+x^(-1/4))²

=x^(1/2)+2x^(1/4)x^(-1/4)+x^(-1/2)

=x^(1/2)+x^(-1/2)+2

=3²=9 -> x^(1/2)+x^(-1/2)=7

Squaring both sides again,

x+2x^(1/2)x^(-1/2)+x^(-1)=49

x+x^(-1)+2=49

x+1/x=47

2.

(i) The easiest way I see to get the radius of the circle is to see that since y=-3 is 2 units below (5,-1), then the higher horizontal tangent will be 2 units above (5,15), which is y=17. So the radius is (17+3)/2=10 units.

(ii) The y-coordinate of the 2 centres is easily found by 17-10=7.

There are multiple ways I see to get the x-coordinate, the fastest that I can see is this:

Let the centre of C2 be (a,7).

See that a-5 is the horizontal distance between C2 and the vertical line cutting through (5,-1) and (5,15).

By Pythagoras theorem, (a-5)²+((15+1)/2)²=10² which gives a-5=6 and a=11.

The x-coordinate of C1 is 5-6=-1.

So the 2 centres are (-1,7) and (11,7)

(iii)Should be fairly straightforward.

3. I think you're missing some info, can't get A.

Edit: Would like to point out that my solution for Q2 lacks rigour, whitecorp's solution would be more 'complete'.