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

Show that 1+1/√2+......+1/√n ≥ √2(n-1) for n ∈N, n > 1

The collection of Venn Diagrams is a set. Is it true or false? Justify your answer.

If z belongs to R then |z| = z. Is it true or false? Justify tour answer.

(x)^m+a(x)^m-1+......+am-1(x)+am=0, ai belongs to R for all i=1,...,m has a root in R only if m is an odd no.
Is this true or false? Justify your answer.

Any system of three linear eaquations in two variables has no solution. Is it true or false? Justify your answer.

When Mr. Ramos died, ⅓ of his state was given to charity and ½ of the remainder to each of his two sons. If each son received P 150,000, what was the value of his state?

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

Floyd is an aspiring music artist. He has a record contract that pays him a base rate of $200 a month and an additional $12 for each album he sells .last month he earned a total of $644. write an equation to determine the number of albums (a) Floyd sold last month. find the number of albums Floyd sold last month.

Prove algebraically that the straight line with equation x=2y+5 is a tangent to the circle with equation x^2+y^2=5