True or false: If a,b,m are integers with m > 0 satisfying m|(a^2 − b^2), then m |(a −b). Justify your answer.

Q: Determine the number of integer solutions for x₁ + x₂ + x3 < 33 where x, 72 X2 2-1 and - 1 ≤ x₂ <19

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Q: In(2x² – 2) = In- 2x2 = 2 In x 2. True False

A: Check whether ln2x2-2=ln2x22=2lnx is true or false as follows. Recall, ln(a)-ln(b)=lnablnxa=alnx

Q: Say whether the following is true or false and support your answer by a proof.…

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Q: (a) How many nonnegative integer solutions are there to the equation ₁ + x₂ + x3 + x₁ = a? (b) How…

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Q: -2{-12/-3+2[2²-12-√100]-(3²)}

A: We want to solve the given basic mathematical operation problem.

Q: If a,b,c,d are in distinct real number in A.P. Such that 2(a-b)+c(b-c) +(c-a) =2(a-d)+(b-d) +(c-d)'…

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Q: Hw/ If 2x, - X2 + 3 X3=2 メi+3X2- メ3=11 2 Xー2×2+ 5X3=3 %3D Then Find The values X, X2

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Q: (2x* + 5x3 + 5x? + 10х + 8) + (x +2)

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Q: 2 fax) = 2 + 3x-xª for f(x+1)

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Q: a. Without tables, show that -(p v (-p ^g)) a nd -p ^-q are logically equivalent.

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Q: 11) 2x+5=5-x

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Q: F6 onal Academy of Science. All Rights Reserved. * Simplify. 21x²y 75xy5 F7 [?] [ ]y] F F8 DELL F9…

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Q: Find the number of nonnegative integer solutions to x₁ + x₂ + x3 + x4 + x5 ≤ 23. Find the number of…

A: We have to find the number of non negative integer solution of Note: According to the guidelines we…

Q: Show the following for [im 11x|lp = 11x11.00 P-0 XER

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Q: 2 4. Express 989 = 23 43 in the form x² + xy + 5y².

A: The given number is 989. The objective is to express the given number in the form of x2+xy+5y2.

Q: Prove that AXB|=A²B² - (AB)².

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Q: If X is the smallest, or first of three consecutive even integers express the sum of all three…

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Q: Prove that m^3 + 2n^2 =36 has no solution in positive integers.

A: Prove that  there is no solution for positive integers.Let if for for

Q: Find the number of positive integers not exceeding 100 that are either odd or the square of an…

A: The objective is to find the number of positive integers not exceeding that are either odd or the…

Q: the number of nonnegative integer solutions to (x₁ + x2 + x3 + x4 + X5) (X6 + X7 + x8 + x9 + x10) =…

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Q: I need help

A: To find:∫013481-u221+u23du

Q: lo) Let x-16 X+4 >メキ-4 K Xニー4

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Q: Prove that if x is an even integer, thenx^2−6x+ 3is odd

A: Any integer of the form 2m+1 is odd.

Q: 3) Find integers x and y such that 13x + 15y = 1.

A: We see, 15 - 13 = 2              =&gt; k(15 - 13) = 2k for any integer k              =&gt; 15 k -…

Q: 32) -3x2 + 3x - 5s0 32) C) (-«, «) D) Ø

A: We want to find domain of the function in which it is always negative or zero.

Q: 3. Show that (5+ 13)e + (5- i3)-" is a real number if is also a real number.

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Q: If A= xe Z:2" = 1 and B = {x e Z:-4 < 3x-1<11}, then find n(A×B),where Z is a set of integers.

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Q: 4. Show that it has a real value!

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Q: c) 2x, +8X2 -Х3 +9х4 =9 X, +3X2 -2х3 +5 Хи 3X, +5Х2 - 12Х3 +17Х4 = 7 че

A: The given system of linear equations…

Q: 6. Solve for x. a) x- 5 = 7 b) 2(x+ 1) = 10 c) 5x – 8 = 2x + 3 d) -5x + 1 = 3x + 2 e) 8 = 4x – 4 f)…

A: Note:- according to the company policy we can attempt ?️ only three subpart of a question so please…

Q: How many integer solutions to x1+ x2+ x3+ x4 = 36 are there for which æ1 > 5, x2 > 3, x3 > 5 and æ4…

A: We have to find the number of solutions to x1+x2+x3+x4=36 for which x1≥5, x2≥3, x3≥5 &amp; x4≥6.

Q: Which of the followings are true (false) in the set of real numbers? A) (Vx) (y) (x+y=10) B) (3x)…

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Q: How many nonnegative integer solutions are there of the equation x1 +x2 +x3 =18?

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