SOLUTION: If {{{x}}} is a root of the quadratic equation {{{x^2=3-2x}}}, show that a) {{{x^3=7x-6}}}, b) {{{x^4=21-20x}}}. I need steps. {{{THANKS!}}}

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: If {{{x}}} is a root of the quadratic equation {{{x^2=3-2x}}}, show that a) {{{x^3=7x-6}}}, b) {{{x^4=21-20x}}}. I need steps. {{{THANKS!}}}      Log On


   

Question 702263: If x is a root of the quadratic equation x%5E2=3-2x, show that
a) x%5E3=7x-6,
b) x%5E4=21-20x.
I need steps. THANKS%21
Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
x is a root of the quadratic equation x%5E2=3-2x, show that
a) x%5E3=7x-6,
b) x%5E4=21-20x.
**
x^2=3-2x
x^2+2x-3=0
(x+3)(x-1)=0
x=-3
or
x=1
..
a) x%5E3=7x-6,
For x=-3
-3^3=7*-3-6
-27=-21-6
-27=-27
..
for x=1
1^3=7*1-6
1=1
..
b) x%5E4=21-20x
for x=-3
(-3)^4=21-20(-3)
81=21+60
81=81
..
for x=1
1^4=21-20(1)
1=1