If t2-t-1-0- then the value of the expression t-1-t - t2-1-t2 - - t27-1-t27 equals

The correct option is A 0 Let S= ( t+1/t )+ ( t^2+1/t^2 )+⋯ + ( t^27+1/t^^27 ) =(t+t^2+............+t^27)+(1t+1t^2+..........+1t^27) =(t(1 ...

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nCr Definitions and Properties

If t2+t+1=0...

Question

If $t^{2} + t + 1 = 0,$ then the value of the expression $(t + \frac{1}{t}) + (t^{2} + \frac{1}{t^{2}}) + \dots + (t^{27} + \frac{1}{t^{^{27}}})$ equals

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Solution

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t^{2} + t + 1 = 0

{(t + \frac{1}{t})}^{2} + {(t^{2} + \frac{1}{t^{2}})}^{2} + . . . . . . . . + {(t^{27} + \frac{1}{t^{27}})}^{2}

t^{2} + t + 1

{(t + \frac{1}{t})}^{2} + {(t^{2} + \frac{1}{t^{2}})}^{2} + . . . . {(t^{27} + \frac{1}{t^{27}})}^{2} = 54

t^{2} + t + 1 = 0

{(t + \frac{1}{t})}^{2} + {(t^{2} + \frac{1}{t^{2}})}^{2} + {(t^{3} + \frac{1}{t^{3}})}^{2} . . . . + {(t^{27} + \frac{1}{t^{27}})}^{2}

t^{2} + t + 1 = 0

{(t + \frac{1}{t})}^{2} + {(t^{2} + \frac{1}{t^{2}})}^{2} + {(t^{3} + \frac{1}{t^{3}})}^{2} . . . . + {(t^{27} + \frac{1}{t^{27}})}^{2}

x = \sqrt{\frac{1 - t^{2}}{1 + t^{2}}}

y = \frac{\sqrt{1 + t^{2}} - \sqrt{1 - t^{2}}}{\sqrt{1 + t^{2}} + \sqrt{1 - t^{2}}},

\frac{d^{2} y}{d x^{2}}

t = 0

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