Algebra Answers

Is the word problem a chef needed 32 plates away in the kitchen. She broke 4 of the plates. How many plates does she have left? A conclusion of 32%4=8?

prove that ((x+y+z)/3)^(x+y+x) <=x^x.y^y.z^z<=((x²+y²+z²)/(x+y+z))^(x+y+z) where x,y,z bleongs to N

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 ∆(fi)=A.
iii) Prove that A∆B= (A∩ B' ) U (A' ∩B)

Let A, B and C be subsets of a set. Prove that , A ∩ B ⊆ C iff A ⊆ B' U C

Use the Cauchy-Schwarz inequality to solve x³-25x²- 4x+ 100= 0 if we know that all its roots are rational.

Use the Cauchy-Schwarz inequality to solve x³-25x²-4x+100=0, if we know
that all its roots are rational.

For any z∈C, if |z| , then ∈R z∈ R . Is it true or false ? Give reasons.

A biquadratic equation must have at least one real root. Is it true or false? give reasons.

Find the value of a for which the polynomial x^5 - ax^2 - ax +1 has −1 as a root with
multiplicity at least 2.

Find the roots of 2x^4 + 9x^3 -9x^2 - 46x +24 by Ferrari’s method.