7. Let r, y E R such that r < 2y. If 2x? + 2y? > 5xy, then 2x < y. [PROOF BY CONTRAPOSITION] (Hint. Consider the factorization of 2x2 - 5xy + 2y?.)

Q: %3D 2. Prove that -24y of 3. =2x

A:

Q: Prove that Σ (2n+1) P(x) no (1-2hx+h²) ¾/2₂

A:

Q: Q2/ fincd lachre trans form for at X- 3x+2X=lee

A: given equationx"-3x'+2x=1-e2tby assuming that initial condition is zero.x"=s2X(s)and x'=sX(s)and…

Q: Let x, y e Z. Prove that if 3x+7y is odd or 5x + 6y is even, then x or y is even.

A: We have given that for x,y belongs to integers. If 3x+7y is odd or 5x+6y is even then x or y is even…

Q: 2 is a counterexample of vxay(x = 1/y), where the domain for all variables consists of all integers.…

A:

Q: 3. Prove that {12a + 4b |a, b e Z} = {4c\c € Z}.

A: as per our guidelines we are supposed to answer?️ only one question. Kindly repost other question as…

Q: 1. Find the 5roots of z1 = -V3+iv3. %3D

A: (As per bartleby guidelines, for multiple questions asked, only the first question will be solved.…

Q: Q3- Give an example of two denes not equal X subsets of (R,T) and (z, of ). ( Explain your answer ).…

A: Answere : The two example are given below :

Q: Prove in detail that Q(/3+ v7) = Q(V3, v7) %3D

A: According to guidelines we solve one question.

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

A:

Q: Let x, y EZ. Prove that 3|xy if and only if 3|x x or 3 y.

A:

Q: Suppose X = (X1, X2, . .. , Xk) ~ Multinomial(n, p) , with p = (p1, P2, ..., Pk), prove that Cov(X;,…

A: Introduction :-  Given that X is a vector of random variable and it follows Multinomial(n,p) Where p…

Q: 18. Let xo < x, < x2, let {yo, y, y2} be given. Find the polynomial q(x) with deg(q) < 2 and such…

A:

Q: 2 2 22 if== prove that 22 a¯x +b¯y¯ +c¯=¯ 3, ,3, 3 a'x + b°y +c°z xyz abc %3D

A:

Q: 1. Given that r + px+q and 4x +q have a factor (x-r) where p,q and r are non-zero. Show that 4p…

A: topic - quadratic equations

Q: 2 5= {(0, 0₂, 93) | DER₁, A₂ER₂, az ER₂ Z Show that sis subring of RxP₂Rz

A: We have to show that S is a subring of ring R1×R2×R3.

Q: Show that for all z1, Z2 E C, Then we have: |Iz1| – |z2|| < |z1 +z2l

A: 2) The inequality can be proved as follows:

Q: (2) Suppose that G, C Zn-r. Then prove that G,-1C Zn-r+1

A: We prove that

Q: %3D n-0o 2n

A: Given. We are given a limit and we need to prove that the limit of the given function at infinity…

Q: Show that 2Z ∪ 3Z is not a subring of Z.

A: Theorem for Sebring Test: For any ring R, a subset S of R is a subring if and only if: it is closed…

Q: 13 3. Use the IVT to prove that y = r Inr has at least one zero on 2 2

A: Above function is continuous function in given interval. So we can apply IVT

Q: Is z(√2) isomorphic to z(√3)?

A:

Q: AE Mmxn amed suppose be non Let that A=xY is the fall ragak factorization that At =x*y then Show

A:

Q: Prove that 1 (c) 2F₁ (a, b; c; z)

A:

Q: The characteristic of Z3[x] is 6. a) True b) False

A: Determine whether the given statement is true or false.

Q: Prove that if x+y=%30 then y=-x

A: See the attachment

Q: 3. Prove that Re(2-+z')<4 when z<1.

A: a.          x+y ≤x + y                                             (triangle inequality)b. Re(z1+z2)…

Q: Solve the followig 13. BauSsian or Eduss Jordan Using E lemination. 5x, +6x=7X 3D0 3. ース×,+ 3X7…

A: Answer

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: _. . Prove that z² = + Emo(-1)" (n + 1) (²2)", where |z-21 < 2.

A:

Q: c If in is an involution of X, show that (x, y)in = (yin, xin) is an involution of X2). %3D

A: Let X be a lattice We have to show that (x, y)in=(yin, xin) is an X[2] X[2] is a 2 x 2 matrix We…

Q: Prove indirectly: "V n E Z, 4 ł (n² – 2)."|

A: Ans:Let us assume that 4/n2-2;∀n∈zthen we have there exist a positive integer k such…

Q: Show that ∗ : R × R → R defined by        a ∗ b = a + 2b is not commutative.

A: Show that ∗ : R × R → R defined by        a ∗ b = a + 2b is not commutative.

Q: Q) prove that (1) -2P xSinx 2.

A: Disclaimer: Since you have posted a question with multiple sub-parts, we will solve the first three…

Q: 1. Prove that fraction where m is z-4

A: Given: zn-1z-1 ⇒zn-1nz-1 ----(1) Let apply the limit in equation (1) limz→1zn-1nz-1 ----(2) Let n=pq…

Q: Prove that {4a + 126 : a, b E Z} = {4c: c € Z}.

A:

Q: Show that 2Z U 3Z is not a subring of Z.

A: show that 2Z∪ 3Z is not a subrings of Z:   Solution:-             Let 2∈ 2Z∪3Z…

Q: how that ℝ3 = span( 1 1 2 1 2 1 0 3 -1

A: We want to show that  any vector can be written as linear combination of the three  given vectors…

Q: Q1) Compute the products using the definition as a linear combination. 8 3 -4 1 2 1 5 1

A: As per the definition of linear combination abcdef.x1x2x3=x1.ad+x2.be+x3.cf

Q: 4. Prove that d x" = nx"-1 ミクー! de

A: To prove that ddx(xn) = nxn - 1

Q: Prove that R (D-1 and R)%=(-)

A: The objective is to prove that  Pn1=1Pn-1=-1n

Q: use the convolution theorem to find L'{2+1 -1 4 Specifically s²(s²+1)

A: Given,        L-14s2s2+1=

Q: E Show that x'+ 3x+ 2 has 4 zerosin Ze

A:

Q: 4. Verify thatf (x) = x³ – x2 – 20x + 6 satisfies the three conditions of Rolle's Theorem on [0,5].…

A:

Q: 3. Prove that (An B)² C A x B.

A:

Q: Show that Z[√−D] is not a unique factorization domain, where D is squarefree and positive

A: Given: To be prove Z-D is not unique factorization domain.

Q: Let x, y e Z. Prove that if 3x + 7y is odd or 5x + 6y is even, then x or y is even.

A:

Q: 1. Use substitution technique to show that ++x+2+x- v2 +C dr 1 In rV+r+2 +x+2+r+ V2

A: As per our guidelines we are supposed to answer only one question that is the first question. For…