Question

Oblicz różnicę odwrotności kwadratów liczb

x= √2/9

y= 0,(2) * √3

Answer 1

0,(2)=0,22222...

x=0,222222...

10x=2,222222...

10x-x=2,222222...-0,2222222

9x=2

x=2/9

 

x^2=(√2/9)^2=2/81

1/x^2=81/2

y^2=(2/9*√3)^2=4/81*3=12/81=4/27

1/y^2=27/4

 

81/2-27/4=162/4-27/4=135/4=33,75

Answer 2

x = √2 / 9

y = 0,(2) * √3 = 2/9 * √3 = 2√3 / 9

 

1/x² - 1/y² = (y² - x²) / (xy)² = ......

 

y² - x² = (2√3 / 9)²  - (√2 / 9)² = 12/81 - 2/81 = 10/81

(x * y)² = (√2 / 9 * 2√3 / 9)² = (2√6 / 81)² = 24/81²

 

1/x² - 1/y² = (y² - x²) / (xy)² = 10/81 : 24/81² = 10/81 * 81² / 24 = 135/4 = 33,75