Question

If x, y, and z satisfy xy=1, yz=2, and xz=3, what is the value of x^2+y^2+z^2? Express your answer as a common fraction.

Answer 1

Step-by-step explanation:

Substitute given value x=3 into the equation xy=1.

y = 1 / x

y = 1 / 3

Substitute the value of y into the equation yz=2.

z = 2 / y

z = 2 / (1 / 3)

z = 2 * 3

z = 6

Now substitute these values into the expression.

x2 + y2 + z2 =

32 + (1 / 3)2 + 62 =

9 + (1 / 9) + 36

Using the LCD of 9.

(81 / 9) + (1 / 9) + (324 / 9)

Now complete the calculation.

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