Please help me with this question.

[Ialwaysneedhelp111]

The geometric mean of two numbers, x and 2x + 1, is the square root of their product. Find x, if their geometric mean is 6. The answers are supposed to be -9/2 and 4

 

[Deleted member 4993]

The geometric mean of two numbers, x and 2x + 1, is the square root of their product. Find x, if their geometric mean is 6. The answers are supposed to be -9/2 and 4

The Geometric mean (GM) should be:

\(\displaystyle GM = \sqrt{x * (2x +1)}\)

continue.....

 

[HallsofIvy]

If the geometric mean is 6 then \(\displaystyle \sqrt{x(2x+1)}= 6\) so, squaring both sides, \(\displaystyle x(2x+ 1)=36\). That gives the quadratic equation \(\displaystyle 2x^2+ x- 36= 0\). That factors or you can solve that using the quadratic formula.