\(\displaystyle{3}{p}{\sin{{x}}}-{\left({p}+{\sin{{x}}}\right)}{\left({p}^{{2}}-{p}{\sin{{x}}}+{{\sin}^{{2}}{x}}\right)}={1}\) has a solution for x. Then

Coradossi7xod

Coradossi7xod

Answered question

2022-03-31

3psinx(p+sinx)(p2psinx+sin2x)=1 has a solution for x. Then number of integral solutions of p are ?

Answer & Explanation

Jadyn Gentry

Jadyn Gentry

Beginner2022-04-01Added 12 answers

On simplifying the the expression is 3psinxp3sin3x=1 which can be written as (p)3+(sinx)3+(1)3=31psinx, i.e a3+b3+c3=3abc form. This means either p+sinx+1=0 or p=sinx=1 Hence possible values of p are 2,1,0,1, i.e 4 integer solutions.

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