Solve by substitution method. y=x^3 +3x^2 +2x

Slovenujozk

Slovenujozk

Answered question

2022-09-02

Solve by substitution method.
y=-x
y = x 3 + 3 x 2 + 2 x

Answer & Explanation

rougertl

rougertl

Beginner2022-09-03Added 16 answers

y =-x............(a)
y = x 3 + 3 x 3 + 2 x...........(b)
now substituting y by -x in equation (b) we get,
x = x 3 + 3 x 3 + 2 x...........(b)
=> x 3 + 3 x 2 + 2 x + x = 0 ................changing sides
=> x 3 + 3 x 2 + 3 x = 0
=> x ( x 2 + 3 x + 3 ) = 0
hence either, x = 0 , hence, y = -x = 0
or
( x 2 + 3 x + 3 ) = 0
using the formula of quadratic equation in ( x 2 + 3 x + 3 ) = 0 , we get,
x = [ 3 ± ( 3 ) 2 4 1 3 ] / 2 1
= [ 3 ± 3 ] / 2
as inside the root the sign is negative hence that will be a complex root, which are,
x = ( 3 ± 3 i ) / 2
hence y = x = ( 3 ± 3 i ) / 2
answer :- x =0;y=0
x = ( 3 ± 3 i ) / 2 ; y = ( 3 ± 3 i ) / 2
Jadon Stein

Jadon Stein

Beginner2022-09-04Added 1 answers

y=x so SUBSTITUTE in x where you see a y.
x = x 3 + 3 x 3 + 2 x. You can divide both sides by xso it becomes
1 = x 2 + 3 x + 2 Subtract one from both sides
0 = x 2 + 3 x + 1 Now use the quadratic formula to find x.You'll get two answers so you need to check both in the second function to see which ones work.

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