SOLUTION: Pleas help out: if the root of the equation{{{4x^2 -8x + 3 =0}}} are A and B, form the equation whose roots are{{{(A + 1/B) and (B + 1/A)}}}

Algebra ->  Radicals -> SOLUTION: Pleas help out: if the root of the equation{{{4x^2 -8x + 3 =0}}} are A and B, form the equation whose roots are{{{(A + 1/B) and (B + 1/A)}}}      Log On


   

Question 978758: Pleas help out: if the root of the equation4x%5E2+-8x++%2B++3+=0 are A and B, form the equation whose roots are%28A+++%2B++1%2FB%29+and+%28B+++%2B++1%2FA%29
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
4x%5E2-8x%2B3=0
4%28x%5E2-2x%29%2B3=0
4%28x%5E2-2x%2B1%29%2B3-4%281%29=0
4%28x-1%29%5E2-1=0
4%28x-1%29%5E2=1
%28x-1%29%5E2=1%2F4
x-1=0+%2B-+1%2F2
x=1+%2B-+1%2F2
A=3%2F2, B=1%2F2
So then,
A%2B1%2FB=3%2F2%2B2=7%2F2
and
B%2B1%2FA=1%2F2%2B2%2F3=3%2F6%2B4%2F6=7%2F6
and
f%28x%29=%28x-5%2F2%29%28x-7%2F6%29
f%28x%29=a%282x-7%29%286x-7%29
f%28x%29=a%2812x%5E2-56x%2B49%29
where a is any non-zero constant