Prove (without stating 7.10 from the chapter notes) that √2+ √5 is not rational.

Q: 4. Solve. A) 3 ()² − 7 (¹) + 4 = 0

A: Since you have posted multiple questions i can do first question as per our company guidelines…

Q: 3. Prove that (v2+ v3) ¢ Q. You can use Prob. 2's result if needed. You may also use the fact,…

A: To prove 2+3∉ℚ That is 2+3 is irrational number Since the sum of two irrational numbers is…

Q: Show v2 is not rational and then conclude that the following set in Q does not have a supremum; A =…

A: We will show root 2 is irrational by first supposing that it is a rational and in the end showing…

Q: Prove that if x is a rational number andy is an irrational number, then x + y is an irrational…

A: As you have asked the problem ( b) only. I have solved this problem in two steps by showing the…

Q: Prove that v7 is irrational. Prove that v7 + 5 is irrational too.

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

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Q: (b) Prove that √2+√3 is irrational. Hint: Assume that √2+√3 is rational. Construct, under this…

A: We write the given expression in single square root form which gives us contradiction.

Q: 3 S ₁² √ (²√₁² - ²√+²) ³ dt

A: Given

Q: 3. Suppose x = (5-√3)¹/3. Show that x is a solution of the equation x6 – 10x³ + 22 = 0. Use the…

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Q: 2. Prove that võ ¢ Q. You may also use the following facts without proof. (1) Each rational number r…

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Q: 9. (a) Prove that v10 is irrational. (b) Use part (a) to prove that v2 + V5 is irrational.

A: To prove the given statements.

Q: (i) Show that √6 + √7 is an algebraic number.

A: We are answering only the first question as per the guidelines. Please repost the other question to…

Q: Show that 15 = x³ + x²e-x + √√x has at least one solution. (Hint: use the Intermediate Value…

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Q: 6. Prove that x is a rational number if and only if 2x - 1 is a rational number.

A: To Prove: x is a rational number if and only if 2x-1 is a rational number.

Q: Based on the graph of f(x) = x³ - 12x² + 47x - 60 shown, what are the real roots of x³-12x²+47x- 60…

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Q: If f(-1)=2x4+x2-5 is -2, can you use the factor theorem to find the other factor? a)No because…

A: Topic:- algebra

Q: Prove that 3√2 is irrational. you may use the proposition that the product of two even integers is…

A: Note: we know that square of an even and an odd integer must be an even and odd integer…

Q: Divide a positive number, say 20, into a sum of two positive rational numbers x, y such that for…

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