Alan

Note: there are many different ways to write the result.  Are you sure what you did is incorrect, or is it just expressed differently from the answer supplied?

\((x^2 + y^2)^2 = x^4 + 2(xy)^2 + y^2\\\\ 1 = \frac{5}{8}+2(xy)^2\)

Can you take it from here?

Have a look at: https://www.youtube.com/watch?v=0KPeDLSLKro 

A short computer program gives 218 for the 100'th green coconut.

                       P(A)              P(B)              P(C)

                         1/3               1/3                1/3

P(green)           6/10             3/9                3/9

                       _________________________

Poverall            1/5               1/9                1/9             P = 1/5 + 1/9 + 1/9 = 19/45

Like so:

As follows:

The areas in the following should help:

As follows:

I'll leave you to crunch the numbers.

2x+ 7 = -5   implies x = -6  since this is less than -2 it is a valid solution

-x^2 - x + 1 = -5  can be written as x^2 + x - 6 = 0  which factors as (x-2)(x+3)=0  for which the only solution that is greater than or equal to -2 is x = 2.

Hence the sum of the valid values of x is -6 + 2 = -4