Algebra Answers

Prove that 1/2 (x+y+z ) <= ( x^2/y+z) +( y^2/x+z)+ ( z^2/x+y) , for x, y, z >0.

Apply the Gaussian elimination process to determine values of lembda for which the following linear system is consistent: x- 3y+4 =0 , 3x-2y=lembda , y= 6- 2x .?

The annual bonus given to the employees of a company is 5 % of their taxable income, after the state and central taxes are deducted. The state tax is 10% of taxable income. The central tax is 20% of taxable income after deducting the state tax . Formulate this situation for determining the bonus, as a linear system?

Solve x^4 -8x^3+21x^2- 20 x +5=0 given that the sum of two of its roots is 4

Find the roots of the equation 2x^3 - x^2 -22 x -24 = 0 , if two of them are in the ratio 3: 4 ?

Find the polynomial over R of least degree which has i-3 and √7 +5i as its roots

Find the sum of 5th roots of unity?

Express z= 1/(-5-i) in standard (algebraic) form. Further, give an Argand diagram in which z , bar z and -z are plotted?

express the following as a single, simplified fraction 25/78 + 9/39 - 11/13

Find x and y , given that (5x+y,3x-y) = (2,2x) belong to Q*Q?