3x^4-12x^2+18=0 then find (x^2-2)^2
Answers
Answer:
Here's the correct answer
Step-by-step explanation:
STEP
1
:
Equation at the end of step 1
((3 • (x4)) + 18) - (22•3x2) = 0
STEP
2
:
Equation at the end of step
2
:
(3x4 + 18) - (22•3x2) = 0
STEP
3
:
STEP
4
:
Pulling out like terms
4.1 Pull out like factors :
3x4 - 12x2 + 18 = 3 • (x4 - 4x2 + 6)
Trying to factor by splitting the middle term
4.2 Factoring x4 - 4x2 + 6
The first term is, x4 its coefficient is 1 .
The middle term is, -4x2 its coefficient is -4 .
The last term, "the constant", is +6
Step-1 : Multiply the coefficient of the first term by the constant 1 • 6 = 6
Step-2 : Find two factors of 6 whose sum equals the coefficient of the middle term, which is -4 .
-6 + -1 = -7
-3 + -2 = -5
-2 + -3 = -5
-1 + -6 = -7
1 + 6 = 7
2 + 3 = 5
3 + 2 = 5
6 + 1 = 7
Observation : No two such factors can be found !!
Conclusion : Trinomial can not be factored
Equation at the end of step
4
:
3 • (x4 - 4x2 + 6) = 0
STEP
5
:
Equations which are never true:
5.1 Solve : 3 = 0
This equation has no solution.
A a non-zero constant never equals zero.