Answer to Question #13621 in Abstract Algebra for Florence

Question

Find the measure, in terms of x, of each side of a square if the Area = x^2– 16x +64.
Factor and solve.
x^2-x-72=0
2x^2+9x-5=0
x^2-64=0
4x^2-36x+72

Answer 1

Area = x^2– 16x +64=(x-8)^2 => the side=x-8

x^2-x-72=(x-9)(x+8)
D=1+72*4=289
x1,1=(1+-17)/2
x1=9, x2=-8

2x^2+9x-5=0
D=81+40=121
x1,2=(-9+-11)/4
x1=-5, x2=1/2


x^2-64=(x-8)(x+8)=0
therefore x1=8, x2=-8

4x^2-36x+72=0
x^2-9x+18=(x-6)(x-3)=0
therefore x1=6, x2=3