Show that V12 is irrational

Q: Find two irrational numbers a and b such that a is rational.

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Q: Q2/ Fin x in the

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Q: Find the domain of u. u (x) = 4 / square root 11- 3x

A: Find the domain of u(x)

Q: If 2x + 3y = à and -x + 5y = 6b, express x and y in terms of à and b.

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Q: Show that r: y = 3. 2n

A: Using two sectant theorem,  ∠n=12x-y  Multiply both sides by 2. ⇒2n=x-y .....(1) Using intersecting…

Q: (b) Prove or disprove: Z10 ~ Z5 x Z₂.

A: We shall solve first question only as you have asked more than one unrelated question. For others…

Q: Show that (x- 3) is a factor of 2.x3 - 2x2 - 17x + 15. Hence express 2x³ – 2.x² – 17x + 15 in the…

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Q: b) Show that XNOT =

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Q: is a solution of 2x-6x2+7x-33D0. 2 Prove that x 1-

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Q: Show that 0 x+1

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Q: Show that $) it gly) 1-y 2

A: Recall: The domain of a function is the set of all possible inputs from the function.

Q: Add the following. Identify NPVE. _2 xa-5x+4 a

A: We know that for the rational functions fxgx,the NVP's are the values where gx=0.

Q: Prove that r - 2 does not split in Q ( V2e*).

A: given   x3-2    and    Q23e2π3i now…

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: 2. Compute the value of | V25–x² dr

A: Given data:   The given integral expression is I=∫0525-x2dx.     Assume x=5sint, and differentiate…

Q: ve that if x5 – 3x4 + 2x

A: Introduction: In an equation, the two expressions are assumed to be equal, as indicated by the…

Q: Show that there is no rational number r satisfying 2r = 3.

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Q: Find the value of ‘v’ in v2 – 2v -15 = 0, if v is a natural number.

A: Given quadratic equation is,

Q: Show by contradiction that if 10x2+ 2 is irrational, then x is irrational. 5

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Q: Show that whether x5 + 10x3 + x + 1 is O(x4) or not?

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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: Show that any positive integer n with n ≥ 4 can be expressed as n = 2x + 5y where x ≥ 0, y ≥ 0.

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Q: Show that r3 + 3x² – 8 is irreducible over Q.

A: Here Q is a field and f(x)= x³+3x²-8 is of degree 3. Then by ROOT TEST we can say that f is…

Q: 2 Show 2 3 / 2

A: We have to solve the matrix.

Q: Do not use a calculator in this question. Find the positive value of x for which (4 + V5)x² + (2 –…

A: 3 Given equation is 4+5x2+2−5x−1=0. We have to find the positive value of x. The solution of the…

Q: Show that x + 5[x²] is 0(x²).

A: This is a problem of complexity.

Q: Show that I [My |X] = 0 and var[My | X] = 0²M.

A: Solution :-

Q: If s is neative, its square must be

A: Given s is negative  s < 0

Q: Does S = {x² + 1,x² – 1, 2x – 1} span P2?

A: we know dimension of P2 is 3 so any set which span P2 must have at least 3 elements. here given set…

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

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

Q: Give a proof by cases that [4x] = [x] + [x + ¼ ]+ [x + ½ ] + [x + ¾ ] %3D

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Q: show that x'-15x +C= O has at most root on E2,2] one

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Q: Show that If 2 is a root of  kx4 - 11x3 + kx2 + 13x + 2 Then K = 3

A: Given,          2 is a root of kx4-11x3+kx2+13x+2 then k=3.

Q: - is a real num 1S y+z= 6, 4x +

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Q: Prove that x -2x+2>0 for value of x.

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Q: Show that V3 +2/6 is an irrational number.

A: A rational number can be represented as pq, where p, q are integers and q≠0. If a number can not be…

Q: (b) Show that xE R, x2 - 4x + 5 > 0.

A: As this is a multiple question type, only first question is to be solved, according to the Bartleby…

Q: Show that 0. x+1

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Q: Supppose that X ~ N (2; 3). Find P (1 < X < 4).

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Q: Given: 5(2x – 8) = 30; Prove: x = 7 -

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Q: Show that the real number V2- 2 is algebraic.

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Q: Prove that the expression 2y2 - 128 is equal to 2(x² + 2) (x² – 2) (x8 + 4x+ + 16) Swer:

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Q: Find s' if s = (4x + 1)2 x² – 2 |

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Q: State the theorem that justifies the statement <6= <7.

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Q: If AJKM~ANKL, find x. 6. x+ 2 K 8. x +7 3.

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Q: -:find sup (A) and inf (A) when A= (y = 2x + 1, x € N, -10 < x < 10}

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Q: The number of units in Z29[x] is

A: Solution by using definition of unit elements

Q: ues of p will 3x(4x+3)=-p have non-real root

A: Given Equation 3x4x+3=-p The value of p is found such that the equation has a non-real root.

Q: nd the supremum of each of the ecimal place.) , 12, 3} .2

A: Introduction: If there exists a real number M ∈R, called an upper bound of A, such that x∈ M for…

Statements and Logic

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