What is the sum of the polynomials? (9x4−13x3−x−7)+(7x3−2x+1) A.) −6x^6+9x^4−3x^2−6 B.)−6x^6+9x^4−x−8 C.)9x^4−6x^3−x−8 D.)9x^4−6
2 answers:
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Answer:
See Explanation
Step-by-step explanation:
(a) Proof: Product of two rational numbers
Using direct proofs.
Let the two rational numbers be A and B.
Such that:
The product:
Proved, because 1/3 is rational
(b) Proof: Quotient of a rational number and a non-zero rational number
Using direct proofs.
Let the two rational numbers be A and B.
Such that:
The quotient:
Express as product
Proved, because 3/4 is rational
(c) x + y is rational (missing from the question)
Using direct proofs.
Let x and y be
Such that:
The sum:
Take LCM
Proved, because 7/6 is rational
<em>The above proof works for all values of A, B, x and y; as long as they are rational values</em>
it just so happen that √2 is an irrational number, so any product with it as a factor, will yield an irrational number as well.
factoid: Ancient Greeks were scared of irrational numbers, and they steered clear from √2.