sin-2-x-sinx-4-3-x-0-pi-equation-sum-of-roots-in-range-

Question Number 141110 by Fikret last updated on 15/May/21

{s i n}^{2} x + s i n x = \frac{4}{3}, x \in [0, π]

e q u a t i o n s u m o f r o o t s i n r a n g e ?

Answered by MJS_new last updated on 15/May/21

s^{2} + s - \frac{4}{3} = 0 \land - 1 ⩽ s ⩽ 1 \Rightarrow s = - \frac{1}{2} + \frac{\sqrt{57}}{6}

\sin x = - \frac{1}{2} + \frac{\sqrt{57}}{6} \land 0 ⩽ x ⩽ π \Rightarrow

x_{1} = \arcsin (- \frac{1}{2} + \frac{\sqrt{57}}{6})

x_{2} = π - \arcsin (- \frac{1}{2} + \frac{\sqrt{57}}{6})

x_{1} + x_{2} = π

Facebook Tweet Pin