Page:Elementary algebra (1896).djvu/485

467 Rh dividing by x^m and rearranging the terms, we have

Now

hence writing z for x+{1}{x}, and giving to p in succession the values 1, 2, 3 \ldots we obtain

and so on; and generally x^m + {1}{x^m} is of m dimensions in z, and therefore the equation in x is of m dimensions.

590. To find the equation whose roots are the squares of those of a proposed equation.

Let f(x)=0 be the given equation; by putting y= x, we have x= y, and therefore the required equation is f(y)= 0.

Ex. Find the equation whose roots are the squares of those of the equation 98 + yx? + pow + ps = 0.

Putting x =y, and transposing, we have (y + p2) Vy =— (py + Ps) 5 whence