Question

X - 2 = 1/3x
Find the values of
X2 + 1/9x2
X4 + 1/81x4

Answer 1

Step-by-step explanation:

x_2=1/3x

x_1/3x=2

3x_x=6

2x=6 then,

x=3,

putting the value of x=3 in i eq

x2=1/9×2

6=1/9×2

54=2=27

putting the value of x=3 in ii eq

3×4=1/81×4

12×81=4

972=2=243

Answer 2

$x^2+\frac{1}{9}x^2=10$

$x^4+\frac{1}{81}x^4=82$

Step-by-step explanation:

Given : Equation $x-2=\frac{1}{3}x$

To find : The values of expression ?

Solution :

First we solve the equation,

$x-\frac{1}{3}x=2$

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

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

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

$x=3$

1) The expression is $x^2+\frac{1}{9}x^2$

$x^2+\frac{1}{9}x^2=(3)^2+\frac{1}{9}(3)^2$

$x^2+\frac{1}{9}x^2=9+\frac{1}{9}\times 9$

$x^2+\frac{1}{9}x^2=9+1$

$x^2+\frac{1}{9}x^2=10$

2) The expression is $x^4+\frac{1}{81}x^4$

$x^4+\frac{1}{81}x^4=(3)^4+\frac{1}{81}(3)^4$

$x^4+\frac{1}{81}x^4=81+\frac{1}{81}\times 81$

$x^4+\frac{1}{81}x^4=81+1$

$x^4+\frac{1}{81}x^4=82$