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NISA [10]
3 years ago
7

Solve the quadratic in form equation x^4-14x^2+45=0

Mathematics
1 answer:
Anastaziya [24]3 years ago
7 1
X⁴-14x²+45=0
(x²) ²-14x²+45=0
let y=x²
y²-14y+45=0
(y-9) (y-5) =0
y=9 or y=5
x²=9 or x²=5
x=±3 or x=±√5
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Find the two smallest possible solutions to part 1a​
bixtya [17]
<h3>Answer: A. 5/12, 25/12</h3>

============================

Work Shown:

12*sin(2pi/5*x)+10 = 16

12*sin(2pi/5*x) = 16-10

12*sin(2pi/5*x) = 6

sin(2pi/5*x) = 6/12

sin(2pi/5*x) = 0.5

2pi/5*x = arcsin(0.5)

2pi/5*x = pi/6+2pi*n or 2pi/5*x = 5pi/6+2pi*n

2/5*x = 1/6+2*n or 2/5*x = 5/6+2*n

x = (5/2)*(1/6+2*n) or x = (5/2)*(5/6+2*n)

x = 5/12+5n or x = 25/12+5n

these equations form the set of all solutions. The n is any integer.

--------

The two smallest positive solutions occur when n = 0, so,

x = 5/12+5n or x = 25/12+5n

x = 5/12+5*0 or x = 25/12+5*0

x = 5/12 or x = 25/12

--------

Plugging either x value into the expression 12*sin(2pi/5*x)+10 should yield 16, which would confirm the two answers.

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3 years ago
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