Prove that if a and b are positive integers and ab is not a square, then √a + √b is irrational

Q: 2) Given Z₁-9-j2 and Z=-4-j1, perform the following operations and express your final answers in…

A: Givenz1=-9-j2z2=-4-j1   We are required to finda. z1+z2b. z1-z2c. z2-z1d. z1×z2e. z1z2

Q: Let a, b e R. Prove that if 15a + 206 = 49, then a and b are not both integers.

A: we have 15a+20b =49 and a and b both are in R  we prove that a and b are not both integers.

Q: ove the statements: e difference of the squares of any two consecutive integers is

A: Introduction: Odd numbers are defined as numbers that cannot be divided into two equal parts. Odd…

Q: Suppose a is a positive real number. Prove that if a is irrational, then √ a is irrational

A: We prove it by method of contradiction

Q: are irrational. Prove that √11-√√7 is irrational." Prove indirectly: "It is known that √7 and √11 a

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Q: Factor each of the following a) x-xー4a b)xペー64

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Q: Prove that √2 + √7 is an irrational number

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Q: Prove that there are no integer solutions to the equation x² = 4y + 3

A: To prove that there are no integer solutions to the equation…

Q: If 0 < a < b, prove that 0 < a2 < b2 and 0 < √a < √b

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Q: 2. Prove that √2 & Q

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Q: Prove that if a > 0, and b is an arbitrary real number then x³ + ax + b= 0 has exactly ne real…

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Q: Taylor is paid on the frst day of the month and $80 is  automatically deducted from her pay and…

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Q: use the fator theerem to determine if X+3 is a x³-8x²+ZIx+18 factor of 3. C. =

A: Given the polynomial x3 + 8x2 + 21x + 18, we have to determine that x + 3 is a factor of the given…

Q: According to Descartes' Rule of Signs, how many positive real solutions are there to the polynomial…

A: Now we will find the correct option.

Q: Find non-zero real number values of a, b, c, and d such that the sum (a + bi) + (c + di) is... -a…

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Q: Prove that the set of numbers Q(√2) = { a+b√2: a, b = Q} is a field.

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Q: Prove that if n is odd, then 3 is not a square in GF(5n).  In other words, prove that there is no…

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Q: Find a counterexample to show that each conjecture is false. The difference of two integers is less…

A: To prove the given conjecture false.

Q: Prove that every perfect square is either a multiple of 5 or of the form 5j - 1 or 5j + 1.

A: Fermat's little theorem states that if p is a prime number, then for any integer a, the number ap −…