Number of solutions of the equation arctan [1/(2x^2 + 1)] + arctan [1/(4x^2 + 1) = arctan 2/x^4 is

A)0

B)1

C)2

D)4

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- September 24th 2008, 07:45 AMfardeen_gen[SOLVED] Number of solutions of arctan equation?
Number of solutions of the equation arctan [1/(2x^2 + 1)] + arctan [1/(4x^2 + 1) = arctan 2/x^4 is

A)0

B)1

C)2

D)4 - September 24th 2008, 09:24 AMSoroban
Hello, fardeen_gen!

Quote:

Number of solutions of the equation: . is

. .

Let: . .[1]

. . Hence: . .[2]

Substitute [1] and we have: .

Take the tangent of both sides:

. .

. .

. .

Substitute [2]:

. .

Multiply by the LCD,

. .

This simpifies to: .

. . which factors: .

Then: .

There are**two**solutions . . . answer (C).