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Anna [14]
3 years ago
7

Find the length of side x in the simplest radical form with a rational denominator​

Mathematics
2 answers:
Natali5045456 [20]3 years ago
7 0

Answer:

Step-by-step explanation:

Recognize that this is a 30-60-90 triangle.  

Write and solve an equation of ratios:

 x         1

------ = ------- (which is the tangent of 30°)

√2       √3  

Then √3*x = √2, and so:

       √2

x = ----------

        √3

Rationalize this as follows:  

      √2*√3        √6

x = ------------- = ------

            3-            3

barxatty [35]3 years ago
3 0

Answer: 10√3 / 3

Step-by-step explanation:

cos 30 = 5 / x

x = 5 / cos 30

= 5 / √3 / 2

= 10 √3

= 10√3 / 3

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Answer:

2 solutions

Step-by-step explanation:

x^4-6x^2-7=0

Replace x^2 by y

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y^2-6y-7=0

D=b^2-4ac= (-6)^2-4*1*(-7)= 36+28=64

sqrtD=8

y1=(-b-sqrtD)/2a=-2/2=-1

y2= (-b+sqrtD)/2a=14/2=7

x^2=-1(n0 roots)    x^2=7 x=sqrt7 or x=-sqrt7

2 roots

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