Let a, b be real numbers such that la], [b] >k> 0. Show that la - bl k² a ≤

Q: Consider f = {(x, y) : x ∈ N and x + y = 5}. Write out some elements of f. What are the domain and…

A: Given: f={(x,y): x∈N and x+y=5} The domain of a function f(x) is the set of all values for which the…

Q: Let r and s be nonnegative real numbers, f(r) = r" and g(r) = r. %3D Find all pairs r and s such…

A: Given that: f(x)=xr           and             g(x)=xs

Q: Let x and y be positive real numbers. Prove that a + y > 2/xy.

A: See solution below

Q: A function f:R →→R, where R is the set of real- ax² + 5x - 8 numbers, is defined by f(x) = Find a +…

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Q: Is defined for some value of s?

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Q: If z = 1 - 2j and w= 2 - 3j, express 2. w in the form a + bj where a and b are real.

A: Given  z=1−2jw=2−3j

Q: Find all triples of integers (x, y, z) that satisfy x² + 2y² = z2.

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Q: Show that the interval [0, 1] is uncountable.

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Q: Show that |Aut(Z2 × Z2)| = 6

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Q: Let a, b be positive real numbers. Prove that a +b< v2(a² +b²).

A: solution:-let a, b are positive real numbersroot mean square(RMS) of a and b =a2+b22arithmetic…

Q: Determine the interval(s) on which x² + 2x-3 > 0. x 1 c. d. a. b. -3 1 x > 1

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