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: Prove that (-1ti3)" + (-1-is3)" has either the value 2n+' or the value -2" if r is any ). integer…

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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: (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: 8. If * is defined as a*b = 3a+b where a and b are real numbers, what is 4*3?

A: Given operation is a*b = 3a+b

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: (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: Help please Disprove the statement  by giving a counterexample :…

A: The given statement is a mathematical proposition that states: For all real numbers a and b, if a is…

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

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

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

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Q: let a,b,c,d,e and f be different positive integers so that a² - b² = c² - d² = e² - f² = 63. Value a…

A: Given:- a,b,c,d,e and f are different positive integers.  also a2-b2=c2-d2=e2-f2=63. To find :- the…

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

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Q: 9) Use the properties of exponents to rewrite the expression in the form kx", where k is a real…

A: Since we only answer up to 3 sub-parts, we’ll answer the first 3. Please resubmit the question and…

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: 8 105 = 8 8 8+102 +. + %3D (1+r)' (1+r)² (1+r)³ ' (1+r)*

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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: If 2 2 5 A- and B-1 3 3 -2 find (AB)-!.

A: Consider the given matrix as A-1=3213 and B-1=253-2

Q: 49. Prove that (a – b) × (a + b) = 2(a × b).

A: The following properties of vectors are used in proving the given identity. a×a=b×b=0a×b=-(b×a)

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: What is L! if 2 1 +. s s-4] 4r A. -2t +e В. -t+ 2e¬7! 3t +e" D. -2t+e" C. 47 3r E. 4t - 2e"

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Q: Prove that the expression 2y2 - 128 is equal to 2(x2+2) (x² – 2) (x³ + 4x* + 16).

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