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If `n` is n odd integer that is greater than or equal to 3 but not a multiple of 3, then prove that `(x+1)^n-x^n-1` is divisible by `x^3+x^2+xdot`

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The correct Answer is:
Thus , ` x^(3) + x^(2) + x "divides" (x +1)^(n) , x^(n) - 1`
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VMC MODULES ENGLISH-COMPLEX NUMBERS -JEE ARCHIVE
  1. If x=a+b,y=a alpha+b beta and z=abeta+ b alpha , where alpha and beta...

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  2. Express 1//(1-costheta+2isintheta) in the form x=i y .

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  3. If n is n odd integer that is greater than or equal to 3 but not a mul...

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  4. The real values of xa n dy for which the following equation is satisfi...

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  5. Let the complex numbers z(1),z(2) and z(3) be the vertices of an equ...

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  6. A relation R on set of complex numbers defined by Z(1)RZ(2) hArr (Z(1)...

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  7. Prove that the complex numbers z(1),z(2) and the origin form an equ...

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  8. If roots of an equation x^n-1=0a r e1,a1,2, a(n-1), then the value of...

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  9. Show that the area of the triangle on the Argand diagram formed by the...

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  10. Complex numbers z(1),z(2)andz(3) are the vertices A,B,C respectivelt o...

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  11. If i z^3+z^2-z+i=0 , where i=sqrt(-1) , then |z| is equal to 1 (b) 1/2...

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  12. If |z|<=1,|w|<=1, then show that |z- w|^2<=(|z|-|w|)^2+(argz-argw)^2

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  13. Find the non-zero complex number z satisfying z =i z^2dot

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  14. Let z1 \and\ z2 be the roots of the equation z^2+p z+q=0, where the co...

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  15. Let barz+bbarz=c,b!=0 be a line the complex plane, where bar b is the ...

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  16. If z(1) and z(2) are two complex numbers such that |z(1)| lt 1 lt |z...

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  17. about to only mathematics

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  18. Let A={theta in (-pi /2,pi):(3+2i sin theta )/(1-2 i sin theta ) is pu...

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  19. Let Z0 is the root of equation x^2+x+1=0 and Z=3+6i(Z0)^(81)-3i(Z0)^(9...

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  20. If z=((sqrt3)/(2)+(1)/(2)i)^5+((sqrt3)/(2)-(i)/(2))^5, then (a)...

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