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Pythagoras Theorem

(y+z)^2 xy ...

Question

\begin{vmatrix}(y+z)^2&xy &zx xy&(x+z)^2&yz zx&yz&(x+y)^2\end{vmatrix} evaluate

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Q. Evaluate each of the following expressions for x = − 2, y = −1, z = 3:
(i)

\frac{x}{y} + \frac{y}{z} + \frac{z}{x}

x^{2} + y^{2} + z^{2} - x y - y z - z x

Q. Find the product

(x + y - z) (x^{2} + y^{2} + z^{2} - x y + y z + z x)

Q. If ax + cy + bz = X, cx + by + az = Y, bx + ay + cz = Z, show that :

(a^{2} + b^{2} + c^{2} - b c - c a - a b) (x^{2} + y^{2} + z^{2}

- y z - z x - x y)

= (X^{2} + Y^{2} + Z^{2} - Y Z - Z X - X Y)

x^{2} + y^{2} + z^{2} - x y - y z - z x = \frac{1}{2} [(x - y)^{2} + (y - z)^{2} + (z - x)^{2}]

.

if x²+ y²+ z²- xy+ yz+ zx = 0 then x+y/z is

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