Also, if the geometric mean of x and 2x is 6. What is the value of x?
2007-05-31 14:34:56 · 2 answers · asked by carrieluver2 1 in Science & Mathematics ➔ Mathematics
See Wikipedia.
If the GM of x and 2x is 6, then
sqrt(x.2x) = 6
sqrt(2)sqrt(x^2) = 6
sqrt(x^2) = 6 / sqrt(2)
sqrt(x^2) = 3.sqrt(2)
So x = plus or minus 3.sqrt(2)
2007-05-31 14:41:00 · answer #1 · answered by Anonymous · 0⤊ 0⤋
Geometric mean = √(AB)
√(x2x) = 6
square both sides
2x² = 36
x² = 18
x = ± 3√2
.
2007-05-31 14:42:44 · answer #2 · answered by Robert L 7 · 0⤊ 0⤋
The geometric mean of a and b is the square root of a times b.
the square root of (x)(2x) is equal to:
x times square root of 2 = 6
by dividing both sides by square root of 2,
x = 6 divided by square root of 2
(Rationalize the denominator, and we get:)
= 3 times the square root of 2
2007-05-31 14:39:21 · answer #3 · answered by heythere 3 · 0⤊ 0⤋
x is the geom. mean between a and b if
a/x = x/b
x/6 = 6/2x
2x^2 = 36
x^2 = 18
x = sq rt 18 = + - 3 sq rt 2
In geometry, the geom mean is positive only.
2007-05-31 14:37:42 · answer #4 · answered by richardwptljc 6 · 0⤊ 0⤋
Boy dont I feel dumb. I am a college grad and I have no idea. X could equal 4, or 12. But I could be totaly wrong. Good luck.
2007-05-31 14:41:11 · answer #5 · answered by Future FBI 2 · 0⤊ 0⤋