Suppose x,y,z are mutually coprime positive integers that solve x2+y2=z2. a) Show why exactly one of x,y and z is even b) assuming a) and that x is odd, show that z-y and z+y are coprime.

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: 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: N.Find the set of values of x for which: w - x-2 x+1 12. Solve the inequality:(x-3)(x+2)(x+4) > C 13…

A: 11)  xx-2>1x+1⇒xx-2-1x+1>0⇒xx+1-x+2x-2x+1>0⇒x2-2x-2x+1>0           1 If x<-1 then…

Q: 1. Write out the dual of: a. Min 3xl + 2x2 + x3 s.t. xl + x2 - x3 = 4 2x2 + x3 < 7 -xl + 3x2 2 6 х1,…

A: The given LPP is: Min 3x1+2x2+x3 Subject to x1+x2-x3=42x2+x3≤7-x1+3x2≥6x1,x2,x3≥0

Q: Show that if x+yi=(a+bi)- is true, then x-yi=(a-bi)-is all real numbers). true (x, y, a, and b are

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Q: How many nonnegative integer solutions are there to the equation Xị + x2 + x3 + x4 + x5 = 40 if we…

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Q: O Show that the secular equation for an arbitrary 2 x 2 matrix ( ) can be solved exactly by a…

A: Please check step 2 for the solution.

Q: Prove there are no natural numbers a and b such that √a+b = √a + √b.c

A: Assume such a,b exists and prove by contradiction

Q: If g(x) = 8x? + 5x + 3, find the simplest formula for the difference quotient if a and h can be any…

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Q: O. Solve a) 2(x-2) x+1 >0 b) 3x x-2 >6

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Q: Factory full, if possible. a) 40a b5-85a?b"

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Q: 3) Suppose that f mx² + ax + bdx = m, a, & b are constants and C is an arbitrary constant. For each…

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Q: Find all integer solutions r, y,p to the equation I+y+x² + y? = p such that p is a prime number.

A: In this equation, two integers and their squares are added on the LHS. Squares of integers are…

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: 2. Factor. a) x² 18x + 81 b) x² - 2x - 15 c) x² + 2x - 24 d) x² + 6x-40 e) x²+x-30 f) x² + 3x-35 g)…

A: Please follow the next step.

Q: If x,y,z are real numbers satisfying the equation 25 (9x* +y° )+9z²-15(5xy+yz+ 3zx )=0 then prove…

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Q: The number of X₁ + X2 + x3 + x4 + X5 + X6 = 12 is C(12+6-1, 12) = C(17, 12). True non-negative…

A: It is known that the number of non-negative integer solutions to the equation: x1+x2+x3+⋯+xn=k is…

Q: Solve

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Q: Consider the following theorem: There do not exist three consecutive odd integers a, b and c such…

A: In the last , I have written the theorem " There does not exist three consecutive odd integers…

Q: 1. Solve the polynomial inequalities a) x2 - 7x + 12.>0 b) x3 + 4x2 -3

A: The solution are next step

Q: A) |2x² + 5x + 1 = 1 B) 12/1 x-1 x+1 C) 5x + | ≥ 1

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Q: Find the number of 5-tuples (a, b, c, d, e) of positive odd integers that are solutions to the…

A: The idea is to transform this into a known counting problem