Alan

As follows:

(-8)² = +64

-8² = -(8²) = -64

"I got the six equations and six unknowns but was intimidated to solve it."

I'm not surprised.  I wouldn't have bothered if I didn't have software available to do it!  Although there is a matrix capability on the web2.0 calculator on the home page here, it just goes up to 4x4 matrices, so wouldn't have helped here.  Probably Wolfram Alpha would do it, but I haven't tried it with this problem.

See https://web2.0calc.com/questions/help-pls_85427#2

Like so:

"You have linear functions p(x) and q(x). You know p(2) = 3, and p(q(x)) = 4x + 18 for all x. Find q(1). "

"kx^2 - 70x + 2k = 0

Find the maximum integral value of k for which the above quadratic equation has two distinct real roots."

First find the value of k that gives exactly one root, then take the nearest integer saller than that.

To find the value of k that gives exactly one root, set the discriminant to zero.  In this case that is:

70^2 - 4*k*2*k = 0

I'll leave you to solve for k etc.

"integral of sin2x√(1-cosx) dx"

"The quantity sqrt(45) + 2*sqrt(5) + sqrt(360)/sqrt(2) can be expressed as sqrtN, where N is an integer. Find N."

sqrt(45) + 2*sqrt(5) + sqrt(360)/sqrt(2) = sqrt(9*5) + 2*sqrt(5) + sqrt(2*5*36)/sqrt(2)

= 3*sqrt(5) + 2*sqrt(5) + sqrt(2)*sqrt(5)*sqrt(36).sqrt(2) 

=  3*sqrt(5) + 2*sqrt(5) + 6*sqrt(5) 

= 11*sqrt(5)  

= sqrt(11^2 * 5) 

= sqrt(605)

N = 605