If $c^{2} + c = - 1$ then the value of $c^{3} + 2 c^{2} + 2 c - 1$ is

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Solution

The correct option is D $- 2$
$c^{2} + c = - 1 \Rightarrow c^{2} + c + 1 = 0 E q u a t i o n = c^{3} + 2 c^{2} + 2 c - 1 ∴ A d d i n g & s u b s t r a c t i n g e q u a t i o n w i t h c^{3} ∴ 2 c^{3} + 2 c^{2} + 2 c - c^{3} - 1 = - c^{3} - 1 (c^{2} + c + 1 = 0) = - 2 (c^{3} = 1, c u b e r o o t o f u n i t y)$

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If c2+c=−1 then the value of c3+2c2+2c−1 is

The correct option is D −2c2+c=−1⇒c2+c+1=0Equation=c3+2c2+2c−1∴Adding&substractingequationwithc3∴2c3+2c2+2c−c3−1=−c3−1(c2+c+1=0)=−2(c3=1,cuberootofunity)

If $c^{2} + c = - 1$ then the value of $c^{3} + 2 c^{2} + 2 c - 1$ is