How to Solve this Equation = Increase your Algebra Skills

[@michaelempeigne3519]

the expression 1 / t means that t has to be a factor of 1. THe RHS says that t would have to be a perfect square. So really the question is what factor of 1 is a perfect square. since the only factors of 1 is 1 x 1. Therefore, the ans is t =1.

[@wesleychildress2327]

Initially square each side of equation yields 1/t^2=t yields t^3=1 yields t=1

[@DarthKalkillus]

Square both sides, 1/t^2 = t. Then multiply both sides by t^2, to get 1 = t^3 Cube root of 1 is either 1 or -1. Substitute to check for real solutions, 1 will work...-1 does not. Way easier to show a student than with rational exponents.

[@OnlyGodalone]

1/t= √t 1/t^2 = t 1= t^3; 1^1/3 =t; t =1^1/3 = r( cos u° +i sin u°); a) 1^1/3 = 1( cos 0° +i sin 0°)^1/3 b) 1^1/3 = 1( cos [(0+2kπ)/3] + i sin[(0+2kπ)/3)] for k= 0,1,2 So the cube roots of 1 are- 1, 1 ( cos (120°) + i sin (120°)), 1( cos( 240°) +i sin( 240°)) or 1, 1*( -1/2+ i √3/2), 1*( -1/2 - i √3/2) rectangular form 1, 1

[@rapidfiregeekforhire9275]

Would this approach be wrong? I started by saying that x = t^(1/2) and subbing that back into the equation leaving me with 1/(x^2) = x, multiplied each side by x^2 leading to 1 = x^3, there is only one value that satisfies this equation 1.

[@davidbrisbane7206]

Here, t = 1 is the real cube root of unity while t = - ½ + i √(3/ 2) and t = - ½ - i √(3/ 2) are the imaginary, or complex cube roots of unity.

[@harrymatabal8448]

Mr David excellent answer

[@davidbrisbane7206]

@@harrymatabal8448 Thanks 😃

[@marlow769]

I think you took around the park in the opposite direction but it worked…you had me worried for a minute or two.

[@bottlesbob]

I mult each side by t giving 1 = t • sqrt(t) Then squared each side giving 1 = t^2 • t 1 = t^3 Last took cubed root giving 1 = t Is this right?

[@poeda6637]

I did: t x 1/t = t x sq rt of t. So 1 = sq rt of t squared so 1= t. Seems simple enough

[@عليالغالب-ك6ن]

We can solve this equation by squaring both sides and get 1/t2 = t which leads to t3=1 ie t =1and _1 ._1 is rejected.. ,t2 squared t ,t3 cubic t

[@hueho9311]

----> 1=t X t X t ----> t=1 Final answer

[@JohnDoe-ok5wo]

(1/t)^2 = (t^1/2)^2 1/t^2 = t 1 = t^3 t = 1 I'll watch and check my answer.

[@davidbrisbane7206]

Yes. I know how to use Wolfram Alpha 😀.

[@botondzalavari4209]

It's sad that you need that for this example

[@davidbrisbane7206]

@@botondzalavari4209 I don't 😂🤣

[@harrymatabal8448]

T=1

[@johnnolen8338]

Sure, t = 1.

[@juan-pt4vc]

+- 1

[@Dragostrange]

Thank you for my happy face. Can I get a sticker?