9514 1404 393
Answer:
23) x = ±3i, ±√2
26) x = 4/3, (-2/3)(1 ± i√3)
Step-by-step explanation:
23) Put in standard form to make factoring easier.
x^4 +7x^2 -18 = 0
(x^2 +9)(x^2 -2) = 0 . . . . factors in integers
Using the factoring of the difference of squares, you can continue to get linear factors in complex and irrational numbers:
(x -3i)(x +3i)(x -√2)(x +√2) = 0
x = ±3i, ±√2
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26) This will be the difference of cubes after you remove the common factor.
81x^3 -192 = 0
3(27x^3 -64) = 0
(3x -4)(9x^2 +12x +16) = 0 . . . . . factor the difference of cubes
The complex roots of the quadratic can be found using the quadratic formula.
x = (-12 ±√(12^2 -4(9)(16)))/(2(9)) = (-12 ±√-432)/18 = -2/3 ± √(-4/3)
Then the three solutions to the equation are ...
x = 4/3, (-2/3)(1 ± i√3)
X = 2 y = 1
y = 5 x= 4
x = -2 y = -7
y= 0 x= -3
1 day = 24 hours
58 days = 24 x 58
= 1392 hours
30 min = 0.5 hour
1392+15+0.5= 1407.5 hours
