Home
Class 12
MATHS
The equation x^3-3/4x=-(sqrt(3))/8 is sa...

The equation `x^3-3/4x=-(sqrt(3))/8` is satisfied by `x=cos((5pi)/(18))` (b) `x=cos((7pi)/(18))` `x=cos((23pi)/(18))` (d) `x=cos((17pi)/(18))`

A

`x=cos((5pi)/(18))`

B

`x =cos((7pi)/(18))`

C

`x=cos((23pi)/(18))`

D

`x=-sin((7pi)/(9))`

Text Solution

Verified by Experts

The correct Answer is:
A, B
Let `x = cos theta`
`rArr 4 cos^(3) theta -3 cos. theta =-(sqrt(3))/(2)`
`rArr cos 3 theta = cos.(5pi)/(6)`
`rArr 3 theta = 2n pi pm (5pi)/(6), n in Z`
`rArr theta =(2n pi)/(3)pm(5pi)/(18),, n in Z`
Put `n=0, theta =(5pi)/(18)`
`n=1, theta =(2pi)/(3)+(5pi)/(18)=(17pi)/(18)`
`theta =(2pi)/(3)-(5pi)/(18)=(7pi)/(18)`
Promotional Banner

Similar Questions

Explore conceptually related problems

The equation x^(3)-(3)/(4)x=-(sqrt(3))/(8) is satisfied by x=cos((5 pi)/(18))( b) x=cos((7 pi)/(18))x=cos((23 pi)/(18))( d) x=cos((17 pi)/(18))

cos((3pi)/(2) +x) cos(2pi+x)[cot(3pi)/(2)-x+cot(2pi+x)]=1

sin ((5 pi) / (18)) - cos ((4 pi) / (9)) = sqrt (3) sin ((pi) / (9))

cos((3pi)/(4)+x)-cos((3pi)/(4)-x) = -sqrt(2)sinx

The value of cos ec((pi)/(18))-sqrt(3)sec((pi)/(18)) is a

Prove that: cos((pi)/(4)+x)+cos((pi)/(4)-x)=sqrt(2)cos x

Prove that: cos((pi)/(4)+x)+cos((pi)/(4)-x)=sqrt(2)cos x

cos^3(x-((2pi)/3))+cos^3x+cos^3(x+((2pi)/3)))=3/4 cos3x