Question

For what volume of the "x" do the number 1, x², 6-x2 taken in the order from a Geometric progression​

Answer 1

Answer:

The answer is $x=\pm \sqrt 2$

Step-by-step explanation:

Concept : If $a,b,c$ are three numbers in G.P., then $b^2=ac$

Here given $1,x^2,6-x^2$ are in G.P.

      $\Rightarrow (x^2)^2=1(6-x^2)\\\Rightarrow (x^2)^2+x^2-6=0\\\Rightarrow (x^2+3)(x^2-2)=0\\\Rightarrow x^2=-3,2$

But we know that $x^2$ can not be negative

      $\Rightarrow x^2=2\\\Rightarrow x=\pm \sqrt 2$