The number of solutions of the equation sin 2 x + ( 2 + 2 x - x 2 ) sin x - 3 ( x - 1 ) 2 = 0 in [ 0 , 2 ] is , and in [ - 2 , 2 ] is then

Question

The number of solutions of the equation $\sin^{2} x + (2 + 2 x - x^{2}) \sin x - 3 {(x - 1)}^{2} = 0 in [0, \frac{π}{2}]$ is $α$ , and in $[- 2 π, 2 π]$ is $β$ then $α + β =___$

Smart Achievers · Accepted Answer

(3)

$(\sin x + 3) (\sin x - {(x - 1)}^{2}) = 0$

Solution

Q.
The number of solutions of the equation $\sin^{2} x + (2 + 2 x - x^{2}) \sin x - 3 {(x - 1)}^{2} = 0 in [0, \frac{π}{2}]$ is $α$ , and in $[- 2 π, 2 π]$ is $β$ then $α + β =___$

Ans.
(3)

$(\sin x + 3) (\sin x - {(x - 1)}^{2}) = 0$

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Solution

Q. The number of solutions of the equation sin2x+(2+2x-x2)sinx-3(x-1)2=0 in [0,π2] is α, and in [-2π,2π] is β then α+β=___

Ans. (3) (sinx+3)(sinx-(x-1)2)=0

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Q.
The number of solutions of the equation $\sin^{2} x + (2 + 2 x - x^{2}) \sin x - 3 {(x - 1)}^{2} = 0 in [0, \frac{π}{2}]$ is $α$ , and in $[- 2 π, 2 π]$ is $β$ then $α + β =___$

Ans.
(3)

$(\sin x + 3) (\sin x - {(x - 1)}^{2}) = 0$