How to use equation solver with conditions

syms x a r  
x =  isolate(-((2*(90 - x)^r - (2*x + 90)^r)*(a + 4)*(r - 1)==0,a)

Is it possible to ask matlab to solve the above equation setting as a condition that "a" is a positive number?

Ideally, I want matlab to return an equation rather than -4 as the solution.

Answer 1

[Star Strider]

Theoretically, yes:

syms x a r  
assume(a > 0)
x =  isolate(-((2*(90 - x)^r - (2*x + 90)^r)*(a + 4)*(r - 1))==0,a)

However,

Error using sym/isolate (line 108)
Unable to isolate 'a' because the equation has no solution.

Note that the equation you posted has an unmatched parenthesis. I added one to get this to work, so be sure all of them are in the correct places, and that you are not using more of them than you need to.

Answer 2

[Walter Roberson]

No. Your equation has three terms multiplied together

-2*(90 - x)^r + (2*x + 90)^r
a + 4
r - 1

in order for the result to equal zero, one of the terms must equal 0. The only term that involves a is a+4 . In order for that to equal 0, a must be -4.

There are two solutions in r: r = 1 or r = -ln(2)/(ln(90 - x) - ln(2*x + 90)) neither of which involve a and so under the positivity constraint would be valid for all positive a other than x = 0 (as 0 gives a division by 0)