Show that if u is an odd integer ,then the equation x2 +x−u=0 has no solution that is an integer.

Q: 1. Show that 12r2 24.x 'ear dr = ea a a² a³

A: To solve the integral, the formula of the "by parts of integration" will be used, that is,∫u v dx =…

Q: Let a and b be positive integers. If ax + by = c has an integer solution (x, y), it is necessarily…

A: Consider the given equation. Find the characteristic for c if a, b are positive integers and ( x, y…

Q: , 回,那 18x 3x? 2. 12x 10a'b 3. 27 -15ab igm 6. = x6-4

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Q: Let (c1, c2) be a solution of the 2 × 2 system a11x1 + a12x2 = 0 a21x1 + a22x2 = 0 Show that for any…

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Q: The set of solutions to z =-V2 - V26 is

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Q: The set of of solution of x2 - 5x+ 6 0 in Z12 is (a ).{2,3,4} d){2,3,6,11} (b) {2,3} (c) {.2,3,6}

A: Hence option (b) is correct.

Q: Verify that v2+ V5 is algebraic over Q.

A: Algebraic number :- An algebraic number is a number that is a root of a non-zero polynomial in one…

Q: Solve for u. u/2 + 3u/4 = u/8

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Q: 4. Find the solution to an 7an-2 + 6am-3 with ao = 9, a1 = 10, and a2 =

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Q: Is the equation Ax = b consistent for all b in R^3? Explain.

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Q: Find a general solution of ди ди 2- + 3 2u ar

A: Given the pde

Q: 3. Show that (1+i) = 2i

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Q: If X is a positive number such that : X² – 10X = 9VX Then X – VX = ?

A: given:x2-10x=9xsquaring both the sides:x4-20x3+100x2=81xwe get x=0, x=1, x=19±372.but for the…

Q: What element corresponds to (2,3) of (A^T) x (B^T)? What element corresponds to (3,1) of (AxB)^T?…

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Q: Show that x = e4t is a solution to x"" – 12x" + 48x' – 64x = 0. Show that x = et is not a solution…

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Q: If (R – {0}, .) = (Q,.) then 1=0 1=-1 -1=0

A: For the given statement

Q: 2 is > 2 of x, the

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Q: 9. Find the general solutions of X' = AX with A =

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Q: Solve for u. u+5=5 ?

A: Multiply with 5 on both sides

Q: Verify that x = C1et + C2 is a solution to x′′ − x′ = 0.

A: To Verify that x = C1et + C2 is a solution to x′′ − x′ = 0.

Q: For which values of a does ax = 1 have a solution in Z5?

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Q: z equals 1 If 1, then וא

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Q: Solve the IVP: X' = AX, where --() 3 1 0 2 -1 0 0 A = 3 and X(0) = -1 2

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Q: 2. If u = x + y + z' - 3xyz, find the value of x- +y+z

A: To find the partial derivative of the given function u(x,y,z)

Q: 1. Show that (a) exp(2±3лi) = -e²; (c) exp(z+лi) = - expz. πί p ( ² + 7² ) = √ = (1 + i); 4 (b) exp

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Q: Prove that if b+ 6 < 0, then x + bx + 5= 0 has at least one real solution.

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Q: Solve the IVP: X' = AX, where -() xw - () 3 -3 1 A = 2 -1 0 1 -1 1 and 7 X(0) 4 3

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Q: of ALL explanatory variables x2, x3,

A: There will be various methods to test the significance of the exploratory variables in the…

Q: Show that e 12-1/31 2+3az| 2re?

A: The given inequality is                                           ∮|z-1|=1ezz+3dz≤2πe2 To prove the…

Q: why. . If C is 6 × 6 and the equation Cx = v is consistent for every v in R', is it possible that…

A: As you asked to do only question number 18 of the page 2.3 , I do that for you.     Let us do…

Q: 4. у' 3D csc х +у сotx

A: Consider the provided differential equation, y'=cscx+ycotx Find the general solution of the…

Q: Show that if Ax = b has more than one solution, then it has infinitely many solutions. (Hint: If x1…

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Q: Show that the equation In(x + 1) = In(x²) has at least two real solutions.

A: we need to show that ln(x+1)=ln(x2) has at least  two real solutions.

Q: 25. If ā = -j and b = 2x +5y, express and y in terms of ā and b.

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Q: Show that o () –1 is an implicit solution to 2 -2y on the interval (-00, 00). Inload our

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Q: For which values of a and m does ax = 1 have a solutionin Z m?

A: To find for which values of a and m does ax=1 have a solution in Zm. Zm=0,1,2,....,m-1 when a=0,…

Q: If z, = 5ej®1 , z, 3e182 , determine all solutions of 01 and 02 so that z, + z2 = 4.

A: Consider the provided question,

Q: show that (AB)-1 = B-1A-1

A: Given matrix A has a order of 2x2 while matrix B has a order of 2x3.

Q: Prove that there is a solution of the equation 2° + x² + 4 = 0, x in R.

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Q: Prove that there are no solutions in integers x and y to the equation 2x2 + 5y² = 14.

A: Two different proofs are given for the given problem as follows :

Q: Express the GCD of (210,162) as a linear combination of 210 and 162.

A: Here, we have to find the GCD of (210, 162) as a linear combination of 210 and 162. For this, we…

Q: JJ. JUA X ABD) 224 ABE) 16 36. g(x)=2x -3x² +5x+3 ACD) 1 АCE) 2 37. h(x)=x -4x³ +3x² +8 ADE) -3 BCD)…

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Q: Show that if A is singular and Ax = b, b = 0, has one solution, then it has infinitely many.

A: Given: A is singular and Ax = b, b = 0

Q: Find the number of integer solutions of X +x, +x, = 10 subject to the conditions given. a. 저20,%…

A: Integer solution

Q: If c > 0, |u| = c is equivalent to u= or u =

A: If c&gt;0, u&gt;c is equivalent to u&lt;-c   or u&gt;c

Q: +prove by indirect method that i X+y >5 then or y>3. x>2

A: We need to prove that if x+y&gt;5 then x&gt;2 or y&gt;3

Q: If x is even and y is odd, show that (x + y)² is odd.

A: Let x is even and y is odd. We prove that is (x+y)2 odd.

Q: Prove the following:  if x^2 = y^2, then x = y or x = -y.

A: Subtract y^2 from both sides.

Q: How many non-negative integer solutions are there for the following equation such that 0 < x1 < 10?…

A:

Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.