Find the values of x for which `3costheta=x^2-8x+19` holds good. – InterviewSolution

InterviewSolution

1.	Find the values of x for which `3costheta=x^2-8x+19` holds good.
Answer» `3cos theta=x^2-8x+19` `rArr3costheta=(x-4)^2+3` Now, `L.H.S. =3costhetale3` or L.H.S. has greatest value 3 But `R.H.S.(x-4)^2+3ge3` or R.H.S.has least value 3 Hence, L.H.S.=R.H.S. when `3costheta=(x-4)^2+3=3` `rArr costheta=1" and "x-4=0` `rArr theta=2n pi " and " x=4," where "in Z`.

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