Question

24. If xy = a, xz = b, and yz = c and none of these quantities is 0. then x^2+ y^2 + z^2 =​

Answer 1

xy = a,. xyz = az,. z = xyz/a

xz = b,. xyz = by,. y = xyz/b

yz = c,. xyz = cx,. x = xyz/c

also abc = xy*xz*yz = (xyz)^2

now

x^2 + y^2 + z^2

= (xyz/a)^2 + (xyz/b)^2 + (xyz/c)^2

= (xyz)^2 ( 1/a^2 + 1/b^2 + 1/c^2)

= (abc)(b^2c^2 + c^2a^2 + a^2b^2)/(abc)^2

= (b^2c^2 + c^2a^2 + a^2b^2)/(abc)

or

bc/a + ca/b + ab/c