Question

if 4x^2+1/9^2=14 2/3 find 2x+1/3x

Answer 1

Answer:

Step-by-step explanation:

1.)  $4x^{2}$+$1/9^{2}$=14 2/3

2.)  $4x^{2}$+0.01=14 2/3

     -0.01  -0.01

3.)  $4x^{2}$=14.66

      /4      /4

4.) $x^{2}$=3.665

5.) $\sqrt{x} ^{2}$=1.91

6.) $x$=1.91

Answer 2

2x + $\dfrac{1}{3x}$ = 4

Step-by-step explanation:

We have,

$4x^{2} +\dfrac{1}{9x^2} =14\dfrac{2}{3}$

To find, 2x + $\dfrac{1}{3x}$ = ?

∴ $4x^{2} +\dfrac{1}{9x^2} =14\dfrac{2}{3}$

⇒ $(2x)^{2} +(\dfrac{1}{3x})^2 =\dfrac{44}{3}$

Using the algebraic identity,

$(a+b)^{2}$ = $a^{2} +b^{2}$ + 2ab

⇒ $a^{2} +b^{2}$  = $(a+b)^{2}$ - 2ab

$(2x +\dfrac{1}{3x})^2-2(2x)(\dfrac{1}{3x}) =\dfrac{44}{3}$

⇒ $(2x +\dfrac{1}{3x})^2-\dfrac{4}{3}=\dfrac{44}{3}$

⇒ $(2x +\dfrac{1}{3x})^2=\dfrac{44}{3}+\dfrac{4}{3}$

⇒ $(2x +\dfrac{1}{3x})^2=\dfrac{44+4}{3}=\dfrac{48}{3}$

⇒ $(2x +\dfrac{1}{3x})^2=16=4^2$

⇒ 2x + $\dfrac{1}{3x}$ = 4

Hence, 2x + $\dfrac{1}{3x}$ = 4