Algebra Answers

Prove that ((x+y+z)/3)^(x+y+z) ≤ x^x y^y z^z ≤ ((x^2+y^2+z^2)/(x+y+z))^(x+y+z)

Prive that ((x+y+z)/3)^(x+y+z) ≤ x^x y^y z^z ≤ ((x^2+y^2+z^2)/(x+y+z))^(x+y+z)

Express sin^x as a linear combination of sin kx and cos kx, k element of Z.

Prove that if a complex number z is an nth root of a real number a , then so
is z .

Write the polar form of 2+i/2-i

Obtain the geometric representation of
((5+i)(7+6i))/3+i

For any two subsets A and B of a set U , we define their symmetric difference to
be A ∆ B = (A \ B) ∪ (B \ A)
i) Check whether ∆ distributes over ∩ .
ii) Show that A∆ fy =A
iii) Prove that A ∆ B =(A ∩ B compliment ) ∪(A compliment ∩ B).

Can Cramer’s rule be used to solve the system A[x] [0]
[ y] =[0]
[ z] [a]
Where A is given and ais not equal to zero

Q1) Elimination Method by Matrix and Gauss Elimination method are same mathod?

solve by gauss elimination method

x+2y+3z=4
2x+3y+4z=5
3x+4y+5z=6

Tom scored 50% in a test.if his actual Mark's were 15.determine the total Mark's of the test.