Use Newton's method with initial approximation x1 = 1
to find x2, the second approximation to the root of the equation
x4 − x − 8 = 0.

X2 + y 2 = 36 x + y = 6 solve the system of equations.

1- is the product of two rational numbers irrational or rational? first, make a hypothesis by multiplying two rational numbers. then, use variables such as x=a/b and y=c/d and the closure property of integers to prove your hypothesis. 2- what do you think the product of a nonzero rational number and an irrational number is? is it rational or irrational? make use of variables, the closure property of integers, and possibly a proof by contradiction to prove your hypothesis. 3- why do we have to specify that the rational number must be nonzero when we determine what the product of a nonzero rational number and an irrational number is? if the rational number were 0, would it give us the same result we found in part b?

Write 5(6x+4)-2(5x-2) in the form a(bx+c) where a,b and c integers and a> 1