Expand (2x4y)2 using algebraic identity Q 1 Q 2 Divide 6 x3 11 x2 − 39 x − 65 by 3 x2 13 x 13 and find the quotient and remainder Q 3 Q 4 Find the value of 432−43× using a suitable algebraic identity Q 5 Expand (2x4y)2 using algebraic identityIdentity Dual Operations with 0 and 1 1 X 0 = X (identity) 3 X 1 = 1 (null element) 2 X1 = X 4 X0 = 0 Idempotency theorem 5 X X = X(ii) (x y) z = x (y z) (associativity of addition) (iii) There is an element 0 ∈ F, called zero, such that x0 = x (existence of an additive identity) (iv) For each x, there is an element −x ∈ F such that x(−x) = 0 (existence of additive inverses) (v) xy = yx (commutativity of multiplication) (vi) (x y) z = x (y z) (associativity of multiplication) (vii) (x y
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(x y z)^3 identity
(x y z)^3 identity- Use the identity x3y3z3−3xyz=(xyz)(x2y2z2−xy−y z−zx) to determine the value of the sum of three integers given the sum of their squares is 110, the sum of their cubes is 684, the product of the three integers is 210, and the sum of any two products (xyyzzx) is 107 enter your answer as an integer, like this 42To find an efficient way of searching for more solutions, we can change the sign of z (without loss of generality) and write equation (1) in the equivalent form x^3 y^3 z^3 = x y z Making use of the algebraic identity x^3 y^3 z^3 = (xyz)^3 3(xy)(xz)(yz) we have (xyz1)(xyz)(xyz1) = 3(xy)(xz)(yz) (2) Letting S denote the sum xyz, the left side is S^3
X1 x2 x3 x1 x2 x3 x1 x2 x3 x1 x2 x3 x1 x2 x3 x1 x2 x3' (x1x2x3)•(x1x2x3') x1 x2 27 Note Colors are used to help you understand the algebraic manipulation Also, the manipulation process is not unique (a) (10 points To get full points, you need to include the detailed algebraic manipulation Proof by using truth table gets atIdentity 2 div curl a = 0 63 • For a(x,y,z) a vector field ∇∇·(∇∇ ×a) = ∂/∂x ∂/∂y ∂/∂z ∂/∂x ∂/∂y ∂/∂z ax ay az = ∂2a z ∂x∂y − ∂2a y ∂x∂z − ∂ 2a z ∂y∂x ∂ ax ∂y∂z ∂2a y ∂z∂x − ∂2a x ∂z∂y = 0 Identity 3 divergence of Uv 64 • Suppose that – U(r) is a Take any Pythagorean triplet ( a, b, c) Multiplying c 6 k − 2, where k is a natural number As an alternative, you can take any standard Pythagorean triple, eg 3 2 4 2 = 5 2, and then multiply through by 5 4 to get which will give an infinite set of solutions x = a 3 − 3 a b 2, y = 3 a 2 b − b 3, z = a 2 b 2
1 Boolean Algebra Chapter 2 3 Z Aliyazici Basic Identities of Boolean Algebra 1 X0 = X 2 X1 = X 3 X1 = 1 4 X0 = 0 5 XX = X 6 XX = X 7 XX' = 1 8You can put this solution on YOUR website!Note the following identity 3 (x 2 y 2 z 2) (x y z) − (x y z) 3 = 2 (x 3 y 3 z 3 − 3 x y z) The question tells us that x 3 y 3 z 3 − 3 x y z = 1 Thus we have 3 (x 2 y 2 z 2) (x y z) − (x y z) 3 = 2 (x y z) 3 (x 2 y 2 z 2) − (x y z) 2 = 2 It is well known that for real numbers the expression inside the square brackets cannot be
Now we plug in all the values in the identity 684 3(210) = (xyz)() 684 630 = (xyz)(3) 54 = 3(xyz) Divide by 3 on both sides 18 = xyz the value of the sum of three integers is 18 New questions in Mathematics I just need the answers to these and I'll be done with my homeworkPlease help heyy ppl u should add me on discord !• x(y z) = xy xz and (x y)z = xz yz for all elements x, y and z of R (the Distributive Law) The first four of these axioms (the axioms that involve only the operation of addition) can be summarized in the statement that a ring is an Abelian group (ie, a commutative group) with respect to the operation of addition Example The set Z of integers is a ring with the usualX 3, 2y – 5, 3x2, 4xy 7 etc You can form many more expressions As you know expressions are formed from variables and constants The expression 2 y – 5 is formed from the variable y and constants 2 and 5 The expression 4 xy 7 is formed from variables x and y and constants 4 and 7 We know that , the value of y in the expression, 2 y – 5, may be anything It can be 2, 5, –3, 0
Solution Verified by Toppr 27x 3y 3z 3−9xyz =(3x) 3y 3z 3−9xyz =(3x) 3y 3z 3−3×3x×y×z using identity a 3b 3c 3−3abc=(abc)(a 2b 2c 2−ab−bc−ca) Putting a=3x,b=y,c=z =(3xyz)(9x 2y 2z 2−3xy−yz−3zx) Ex 25, 13 If x y z = 0, show that x3 y3 z3 = 3xyz We know that x3 y3 z3 3xyz = (x y z) (x2 y2 z2 xy yz zx) Putting x y z = 0, x3 y3 z3 3xyz = (0) (x2 y2 z2 xy yz zx) x3 y3 z3 3xyz = 0 x3 y3 z3 = 3xyz Hence proB) and are associative for all x, y and z in B, x(yz)=(xy)z, and x(yz)=(xy)z c) and are distributive over one another x(yz)=xyxz, and x(yz)=(xy)(xz) d) Identity laws 1x=x1=x and 0x=x0=x for all x in B e) Complementation laws xx'=1 and xx'=0 for all x in B Examples
Hence, x 2 y 3 z ≤ 14 x 2y 3z \leq \sqrt{14} x 2 y 3 z ≤ 1 4 with equality holding when x 1 = y 2 = z 3 \frac{x}{1} = \frac{y}{2} = \frac{z}{3} 1 x = 2 y = 3 z Together with x 2 y 2 z 2 = 1 x^2 y^2 z^2 = 1 x 2 y 2 z 2 = 1 , we get (xy)^3 (yz)3 (zx)^3 = 3(xy)(yz)(zx) That is it no constraints etc It mentions "This can be done by expanding out the brackets, but there is a more elegant solution" Homework Equations The Attempt at a Solution First of all this only seems to hold in special cases as I have substituted random values for x,y and z and they do not agree It seems more like this Stack Exchange network consists of 178 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers Visit Stack Exchange
Get a quick overview of Algebraic Identity of (xy)³ and (xy)³ from More Complex Identities in just 3 minutesUsing the identity `x^3 y^3 = (x y)(x^2 xy y^2)` We get `27y^3 125z^3` `= (3y 5z)(3y)^2 3y\xx5z (5z)^2` `= (3y 5z)(9y^2 15yz 25z^2)` (ii) `64m^3 343n^3` Answer Given; Use the identity x^3y^3z^3−3xyz=(xyz)(x^2y^2z^2−xy−yz−zx) to determine the value of the sum of three integers given the sum of their squares is 110, the sum of their cubes is 684, the product of the three integers is 210, and the sum of any two products (xyyzzx) is 107 1 See answer Advertisement Advertisement leighannmfral is waiting for your help Add your
Answer (1 of 5) We are given with the equation x^3 y^3 z^3 3xyz let this equation be called 1 We are given values of x = 0, 2*100,2*10^2 y = 4*10^2 z = 6*10^2 Now put the values in the equation 1 (2*10^2)^3 (4*10^2)^3 (6*10^2)^3 3*(2*4*6*10^(2*3)) (8*10^6)Click here👆to get an answer to your question ️ Expand (4x 2y 3z)^2 using identity Join / Login >> Class 9 >> Maths >> Polynomials >> Algebraic Identities >> Expand (4x 2y 3z)^2 usi Question Expand (4 x − 2 y − 3 z) 2 using identity Easy Open in App Solution Verified by Toppr (4 x − 2 y − 3 z) 2 We know that (x y z) 2 = x 2 y 2 z 2 2 x y 2 y z 2 x zThe values of x, y, z in order of the system of equations 3x y 2z = 3, 2x – 3y – z = –3, x 2y z = 4, are (a) 2, 1, 5 (b) 1, 1, 1 (c) 1, –2, –1 (d) 1, 2, –1 Ans (d) Related Mole problems with solutions Ques If a matrix A is such that 3A 3 2A 2 5A I = 0 then its inverse is (a) –(3A 2 2A 5I) (b) 3A 2 2A 5I (c) 3A 2 – 2A – 5I (d) None of these Ans (a