(2x^2-7)^(1/2)=x

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Solution for (2x^2-7)^(1/2)=x equation: 


D( x )

2*x^2-7 < 0

2*x^2-7 < 0

2*x^2-7 < 0

2*x^2 < 7

2*x^2 < 7 // : 2

x^2 < 7/2

x^2 < 7/2 // ^ 1/2

abs(x) < (7/2)^(1/2)

x in (-(7/2)^(1/2):(7/2)^(1/2))

x in (-oo:-(7/2)^(1/2)> U <(7/2)^(1/2):+oo)

(2*x^2-7)^(1/2) = x // - x

(2*x^2-7)^(1/2)-x = 0

(2*x^2-7)^(1/2) = -x // + x

(2*x^2-7)^(1/2) = x // ^ 2

abs(2*x^2-7) = x^2 // - x^2

abs(2*x^2-7)-x^2 = 0

x in (-oo:+oo)

abs(2*x^2-7)

2*x^2-7 >= 0

2*x^2 >= 7

2*x^2 >= 7 // : 2

x^2 >= 7/2

x^2 >= 7/2 // ^ 1/2

abs(x) >= (7/2)^(1/2)

x in (-oo:-(7/2)^(1/2)> U <(7/2)^(1/2):+oo)

x in (-oo:-(7/2)^(1/2)> U <(7/2)^(1/2):+oo)

2*x^2-x^2-7 = 0

x in (-(7/2)^(1/2):(7/2)^(1/2))

7-(2*x^2)-x^2 = 0

abs(2*x^2-7)-x^2 = 0


/
| 7-(2*x^2)-x^2 = 0 i x in (-(7/2)^(1/2):(7/2)^(1/2))
| 2*x^2-x^2-7 = 0 i x in (-oo:-(7/2)^(1/2)> U <(7/2)^(1/2):+oo)


x in (-(7/2)^(1/2):(7/2)^(1/2))

7-(2*x^2)-x^2 = 0

-3*x^2 = -7 // : -3

x^2 = 7/3

x^2 = 7/3 // ^ 1/2

abs(x) = (7/3)^(1/2)

x = (7/3)^(1/2) or x = -(7/3)^(1/2)

x in (-oo:-(7/2)^(1/2)> U <(7/2)^(1/2):+oo)

2*x^2-x^2-7 = 0

1*x^2 = 7 // : 1

x^2 = 7

x^2 = 7 // ^ 1/2

abs(x) = 7^(1/2)

x = 7^(1/2) or x = -7^(1/2)

x in { (7/3)^(1/2)} 

x in { -(7/3)^(1/2)} 

x in { 7^(1/2), -7^(1/2) }

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