Solve for x

[nycmathguy]

Last question for Sunday night.

Solve for x.

 

[MathLover1]

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

............square both sides

x-1/x=x^2/4............both sides multiply by 4x

4x^2-4=x^3
x^3-4x^2+4=0

Solutions:
x≈-0.90321
x≈1.1939
x≈3.7093

verify solutions:
x≈-0.90321
2*(-0.90321-1/-0.90321)^(1/2)=-0.90321
2*(-0.90321+1/0.90321)^(1/2)=-0.90321
2*0.4516 =-0.90321 => false , so disregard x≈-0.90321

x≈1.1939
2sqrt(1.1939-1/1.1939)=1.1939
2*0.59695=1.1939
1.1939=1.1939->true

x≈3.7093

2sqrt(3.7093-1/3.7093)=3.7093
2(1.8546448054782267)=3.7093
3.7092896109564534=3.7093
3.7093=3.7093 ->true

solutions are: x≈1.1939, x≈3.7093

 

[nycmathguy]

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

View attachment 3816

View attachment 3817

View attachment 3818............square both sides

x-1/x=x^2/4............both sides multiply by 4x

4x^2-4=x^3
x^3-4x^2+4=0

Solutions:
x≈-0.90321
x≈1.1939
x≈3.7093

verify solutions:
x≈-0.90321
2*(-0.90321-1/-0.90321)^(1/2)=-0.90321
2*(-0.90321+1/0.90321)^(1/2)=-0.90321
2*0.4516 =-0.90321 => false , so disregard x≈-0.90321

x≈1.1939
2sqrt(1.1939-1/1.1939)=1.1939
2*0.59695=1.1939
1.1939=1.1939->true

x≈3.7093

2sqrt(3.7093-1/3.7093)=3.7093
2(1.8546448054782267)=3.7093
3.7092896109564534=3.7093
3.7093=3.7093 ->true

solutions are: x≈1.1939, x≈3.7093

What on earth was I thinking posting this Godzilla problem?

 

[MathLover1]

I don't know where did you find it

 

[nycmathguy]

I don't know where did you find it

I found this problem on YouTube. The person explaining this problem is a horrible tutor. I didn't understand one single word.