4. [Disproof by Counter Example] Prove that the following statements are false. a) x²=4 => x=2. b) For all real values of a and b, a-b>0 a²-b² >0. c) The sum of two unequal, positive, irrational numbers is irrational. d) The product of two unequal, positive, irrational numbers is irrational.

Q: Select two positive integers a and b with 5 <  a  ≤  20  and 5  <  b ≤  20.

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Q: Derive one-one correspondence between the real numbers in (0,1) and the set of irrational numbers in…

A: Both the sets that is real number in 0,1 and the set of irrational numbers in 0,1 are uncountable as…

Q: 2. Let b and c be rational numbers and consider the quadratic equation a2+ba +c = 0, with solutions…

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Q: at a, b and c be real numbers such that a #0 and ac+bc+c 4ac.

A: Given data is : a , b and c are real number such that a≠0 and ac+bc+c2&lt;0 Show that b2&gt;4ac

Q: Solve. 7) 2x = /3x + 4 Зx +

A: Square both sides and solve the quadratic equation. Take care of one thing that when we squaring an…

Q: Show that V12 is irrational

A: A Rational Number is a number that can be written in terms of P/Q.  An irrational number can not be…

Q: ;) 2r-11x-21 0 ii) x + x 22

A: 1)                                          2X2-11X-21 =0                         To solve this…

Q: 3. If the expression was placed in the form ax where a and b are real numbers, then which of the 2x…

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Q: sing direct proof, prove the following statements: 1. Prove: If x2-4=0, then x = 2 or x = -2. 2. If…

A: follow next step

Q: Disprove the statement: There is a real number x such that xº +x* +1 = 2x².

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Q: \/(r2 – 6r + 9)    a. Defined for all reals.              b.      r 3   c. r -3…

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Q: Which of the following expressions is equivalent to for all positive real numbers x and y ?

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Q: b.) 3x-2y < 12

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Q: Prove the following statements: (a) The product of two rational numbers is a rational number. (b)…

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Q: a) From the set {-6+2i,  -2.135,  -8, ¾,  √(-16),  √5,   3,  4i,   -1/5} i) List the set of…

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Q: 2-2 Given the equation 2x-1 = -2, -2, which of the following statements is true?

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Q: j2 -j3 2 Determine 1+j)

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Q: Are there numbers a and b such that |a + b| &gt; |a|+|b|?

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Q: Determine: 1 (1 -1 2] [2 3] +0 1

A: given  1-124-1023+1001-1-1 solution we will use property of matrix multiplication and addition to…

Q: Check if the following statement is TRUE or FALSE. 2 Let X and Y be two real numbers satisfying x² +…

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Q: Show that (x? + y²)² = (x² – y²)² + (2xy)? for all real numbers x and y.

A: We have to prove algebraically that x2+y22=x2-y22+2xy2 Simplifying both the sides , we get Here ,…

Q: Simplify. (²) ² [(15+)-9]

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Q: Let a and b be rational numbers. Show that Q(√a, √b) = Q(√a + √b).

A: Given Data Let a and b be a rational number.   Suppose a and b be a rational number. So, √a ϵ Q and…

Q: Let Q be the set of all rational numbers. Which of these equations has no solution in Q? I: x? – 2 =…

A: Given equation are

Q: if a and b are positive real number, then 0<(ab)1/2<=(a+b)/2.

A: If a and b are the positive real number Then we have to prove that  0&lt;ab≤a+b2 Since, a and b be a…