Not Algebra????

Find the roots of

x^2+(4x^3-3x)^2=1

10 Answers

1
Little Angel ·

Can we do it by quadratic eqn method i.e is

x2+16x6+9x2 - 24x4 -1 = 0
and then dividing it by x3 to get a quadratic eqn .????????

This ques seems to be more of Algebra and less of trignometry.

62
Lokesh Verma ·

That will be too difficult to handle..

see the expression closely.. it is very much trigonometry..

1
xYz ·

x =cos8...that thing is cos38

1
Arshad ~Died~ ·

just replace x by cos@
we get
(cos@)^2 +(cos(3@))^2=1

1
xYz ·

cos(npi/4 +- pi/8)

341
Hari Shankar ·

it will be ± cos π/4 and ±cos π/8. Is that what u r trying to say?

1
xYz ·

sir but by assuming x=cos@ ....am i not restricting the domain of function

341
Hari Shankar ·

it is for you to justify your choice then. :D

But again, I like your question.

So tell us what allows you to conclude that by setting x = cos θ we are not excluding any real solutions.

1
xYz ·

like if i substitute so, x can never exceed 1.......if i had to substitute x as some tan or cot ,i wud happily do it...as they give all real values...

341
Hari Shankar ·

If x2 + (some +ve term) = 1, can x2 exceed 1?

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