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The value of x that satisfies the relati...

The value of x that satisfies the relation `x=1 -x+x^2-x^3+x^4-x^5+….oo is `

A

`2 cos 36^@`

B

`2 cos 144^@`

C

`2 sin 18^@`

D

`2 cos 18^@`

Text Solution

Verified by Experts

The correct Answer is:
C
`x=1-x+x^(2)-x^(3)+x^(4)-x^(5)+..oo`
`thereforex=1/(1+x)`
`rArrx^(2)+x-1=0`
`rArrx=(-1pmsqrt5)/2`
But for infinite G.P., x=`(-1-sqrt5)/(2)` is rejected.
`thereforex=(-1+sqrt5)/2=2sin18^(@)`
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