Question

If 2x + (9/x) = 9, then what is the minimum value of x2 + (1/x2)?

Answer 1

MBBS is lakhs his ikan ebbs hajj a bash nano za own

Answer 2

Answer:

Minimum value of given expression is 2.7 (approx.)

Step-by-step explanation:

Given equation : $2x+\frac{9}{x}=9$

To find: Minimum value of $x^2+\frac{1}{x^2}$

To find minimum value of given expression we first find value of x from given equation.

consider,

$2x+\frac{9}{x}=9$

$\frac{2x^2+9}{x}=9$

$2x^2+9=9x$

$2x^2-9x+9=0$

$2x^2-6x-3x+9=0$

$2x(x-3)-3(x-3)=0$

$(2x-3)(x-3)=0$

$2x-3=0\:\:\:and\:\:\:x-3=0$

$x=\frac{3}{2}\:\:\:and\:\:\:x=3$

Now we find value of given expression for both value of x

when x = 3

we get,

$3^2+\frac{1}{3^2}$

$\implies9+\frac{1}{9}$

$\implies9.1\,(approx.)$

when x = $\frac{3}{2}$

we get,

$(\frac{3}{2})^2+\frac{1}{(\frac{3}{2})^2}$

$\implies\frac{9}{4}+\frac{4}{9}$

$\implies2.7\,(approx.)$

Therefore, Minimum value of given expression is 2.7 (approx.)