1. Solve for x. Verify the solution with a graph. 

`*`(`+`(x, `-`(3)), `*`(`+`(x, `-`(2)))) = `*`(`^`(`+`(x, `-`(4)), 2)); x = `/`(10, 3); `*`(`+`(x, `-`(3)), `*`(`+`(x, `-`(2)))) = `*`(`^`(`+`(x, `-`(4)), 2));  

`*`(`+`(x, `-`(3)), `*`(`+`(x, `-`(2)))) = `*`(`^`(`+`(x, `-`(4)), 2)); (3.1.1)
 

 

Plot_2d
 

 

 



 

 

`*`(`+`(x, `-`(3)), `*`(`+`(x, `-`(2)))) = `*`(`^`(`+`(x, `-`(4)), 2));  

`*`(`+`(x, `-`(3)), `*`(`+`(x, `-`(2)))) = `*`(`^`(`+`(x, `-`(4)), 2)); (3.1.2)
 

 

`/`(4, 9) = `/`(4, 9); (3.1.3)
 

 

Image 

Screen Shot of Evaluate a a point Window. 

 

 

 

 

`+`(`/`(55, 36), `-`(`*`(`/`(1, 36), `*`(x)))) = 1;  

`+`(`/`(55, 36), `-`(`*`(`/`(1, 36), `*`(x)))) = 1; (3.1.4)
 

 

x = 19; (3.1.5)
 

 

 

 

`+`(`/`(55, 36), `-`(`*`(`/`(1, 36), `*`(x)))) = 1;  

`+`(`/`(55, 36), `-`(`*`(`/`(1, 36), `*`(x)))) = 1; (3.1.6)
 

 

Plot_2d
 

Plot_2d
 

 

Using Plot from the Context Panel does not show the point of intersection. Better to use the plot command.  

 

plot([`+`(`/`(55, 36), `-`(`*`(`/`(1, 36), `*`(x)))), 1], x = -5 .. 25, y = -1 .. 2, color = [red, blue]);  

Plot_2d
 

 

 

 

solve(`+`(sqrt(`+`(x, 3)), sqrt(`+`(`*`(2, `*`(x)), `-`(3)))) = 6, x);  

6; (3.1.7)
 

 

plot([`+`(sqrt(`+`(x, 3)), sqrt(`+`(`*`(2, `*`(x)), `-`(3)))), 6], x = -5 .. 25, y = -1 .. 10, color = [red, blue]);  

Plot_2d
 

. `*`(To, `*`(check, `*`(numerically))); -1 

 

`+`(sqrt(`+`(x, 3)), sqrt(`+`(`*`(2, `*`(x)), `-`(3)))) = 6;  

`+`(sqrt(`+`(x, 3)), sqrt(`+`(`*`(2, `*`(x)), `-`(3)))) = 6; (3.1.8)
 

 

`+`(`*`(2, `*`(sqrt(9)))) = 6; (3.1.9)
 

 

6 = 6; (3.1.10)
 

 

 

 

`+`(`/`(`*`(`+`(`-`(`*`(b, `*`(m))), a)), `*`(m, `*`(x))), `-`(`/`(`*`(`+`(`-`(`*`(b, `*`(n))), c)), `*`(n, `*`(x))))) = 1; x = `/`(`*`(`+`(`*`(a, `*`(n)), `-`(`*`(c, `*`(m))))), `*`(m, `*`(n)));  

`+`(`/`(`*`(`+`(`-`(`*`(b, `*`(m))), a)), `*`(m, `*`(x))), `-`(`/`(`*`(`+`(`-`(`*`(b, `*`(n))), c)), `*`(n, `*`(x))))) = 1;  

`+`(`/`(`*`(`+`(`-`(`*`(b, `*`(m))), a)), `*`(m, `*`(x))), `-`(`/`(`*`(`+`(`-`(`*`(b, `*`(n))), c)), `*`(n, `*`(x))))) = 1; (3.1.11)
 

 

`+`(`/`(`*`(`+`(`-`(`*`(b, `*`(m))), a), `*`(n)), `*`(`+`(`*`(a, `*`(n)), `-`(`*`(c, `*`(m)))))), `-`(`/`(`*`(`+`(`-`(`*`(b, `*`(n))), c), `*`(m)), `*`(`+`(`*`(a, `*`(n)), `-`(`*`(c, `*`(m)))))))) = 1... (3.1.12)
 

 

1 = 1; (3.1.13)
 

 

 

 

 

tan(x) = cot(x);  

tan(x) = cot(x); (3.1.14)
 

 

`+`(`*`(`/`(1, 4), `*`(Pi))), `+`(`-`(`*`(`/`(1, 4), `*`(Pi)))), `+`(`*`(`/`(3, 4), `*`(Pi))), `+`(`-`(`*`(`/`(3, 4), `*`(Pi)))); (3.1.15)
 

 

tan(x) = cot(x);  

tan(x) = cot(x); (3.1.16)
 

 

Plot_2d
 

 

plot([tan(x), cot(x)], x = `+`(`-`(Pi)) .. Pi, y = -2 .. 2, color = [red, blue], discont = true);  

Plot_2d
 

The image constructed with the plot command is a bit cleaner.   

 

Testing one of the solutions: 

 

tan(x) = cot(x);  

tan(x) = cot(x); (3.1.17)
 

 

1 = 1; (3.1.18)
 

 

`+`(abs(`+`(x, `-`(8))), `-`(abs(`+`(x, 8)))) = 5;  

`+`(abs(`+`(x, `-`(8))), `-`(abs(`+`(x, 8)))) = 5; (3.1.19)
 

 

[[x = -`/`(5, 2)]]; (3.1.20)
 

`+`(abs(`+`(x, `-`(8))), `-`(abs(`+`(x, 8)))) = 5;  

`+`(abs(`+`(x, `-`(8))), `-`(abs(`+`(x, 8)))) = 5; (3.1.21)
 

 

Plot_2d
 

`+`(abs(`+`(x, `-`(8))), `-`(abs(`+`(x, 8)))) = 5;  

`+`(abs(`+`(x, `-`(8))), `-`(abs(`+`(x, 8)))) = 5; (3.1.22)
 

 

5 = 5; (3.1.23)
 

 

 

`+`(ln(`+`(x, `-`(3))), ln(`+`(x, `-`(2)))) = ln(`+`(`*`(4, `*`(x)), `-`(12)));  

`+`(ln(`+`(x, `-`(3))), ln(`+`(x, `-`(2)))) = ln(`+`(`*`(4, `*`(x)), `-`(12))); (3.1.24)
 

 

[[x = 6]]; (3.1.25)
 

`+`(ln(`+`(x, `-`(3))), ln(`+`(x, `-`(2)))) = ln(`+`(`*`(4, `*`(x)), `-`(12)));  

`+`(ln(`+`(x, `-`(3))), ln(`+`(x, `-`(2)))) = ln(`+`(`*`(4, `*`(x)), `-`(12))); (3.1.26)
 

 

Plot_2d
 

 

 

#) + ) = ln(`+`(`*`(4, `*`(x)), `-`(12))); `*`(`+`(x, `-`(3)), `*`(`+`(x, `-`(2)))); = `+`(`*`(4, `*`(x)), `-`(12)); `+`(`*`(`^`(x, 2)), `-`(`*`(9, `*`(x))), 18) = 0 implies x = 3, x = 6.; #Why is  3  omitted as a valid answer? 

eval([`+`(ln(`+`(x, `-`(3))), ln(`+`(x, `-`(2)))), ln(`+`(`*`(4, `*`(x)), `-`(12)))], x = 3);  

Error, (in ln) numeric exception: division by zero
 

 

 

`+`(ln(`+`(x, `-`(3))), ln(`+`(x, `-`(2)))) = ln(`+`(`*`(4, `*`(x)), `-`(12)));  

`+`(ln(`+`(x, `-`(3))), ln(`+`(x, `-`(2)))) = ln(`+`(`*`(4, `*`(x)), `-`(12))); (3.1.27)
 

 

`+`(ln(3), `*`(2, `*`(ln(2)))) = ln(12); (3.1.28)
 

 

2.4849 = 2.4849; (3.1.29)