First solve q(x,y,z)= 2 mod 8, then use Hensel's Lemma to lift to a solution in Z2. When working with quadratic forms in characteristic 2, usually it helps to work mod 8. A good reason ... Simultaneous equations, in 4 unknowns.

Expand (x−y−z)(x−y−z) (x - y - z) (x - y - z) by multiplying each term in the first expression by each term in the second expression. x⋅x+x(−y)+x(−z)− yx−y(−y)−y(−z)− zx−z(−y)− z(−z) x ⋅ x + x (- y) + x (- z) - y x - y (- y) - y (- z) - z x - z (- y) - z (- z) Simplify each term. Tap for more steps...

2023年5月4日 · The expression to make a true equation: (xyz)² - 1 = (____) x (xyz - 1) is (xyz + 1) using difference of two squares. Considering two numbers a and b, the difference of their squares written as a² - b² is equal to the the product of the sum of the numbers and the difference of the numbers, that is (a + b) (a - b).

Reduce the expression by cancelling the common factors. Tap for more steps... Free math problem solver answers your algebra, geometry, trigonometry, calculus, and statistics homework questions with step-by-step explanations, just like a math tutor.

Define f(x, y, z) = √x2 + y2 + z2, which is what we want to minimize, with the constraint g(x, y, z) = xyz2 = 2. We get three equations (I'm using f as shorthand to avoid the messy root): We get y = ± x, z = ± √2 ⋅ x and with the constraint only y = x will work. Finally we get x = ± 1 and this gives us 4 points ± (1, 1, √2) and ± (1, 1, − √2).

Find the shortest distance from the origin to the surface of $xyz^2=2$, i.e. minimize $f (x,y,z)=x^2+y^2+z^2$ subject to $xyz^2-2=0$ hence we obtain $L (x,y,z,\lambda)=x^2+y^2+z^2+\lambda (xyz^2-2)$,t...

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What is (xyz)^2 ?

Free math problem solver answers your algebra, geometry, trigonometry, calculus, and statistics homework questions with step-by-step explanations, just like a math tutor.

If x+y=18, y+z=24 and z+x=22, then find the value of (x2 +y2 +z2 +2xy+2yz+2zx).