Answer:
The number are [tex]\sqrt{6}[/tex] and [tex]\sqrt{6}[/tex] .
Step-by-step explanation:
Given as :
The difference between the squares of two number = 3
And , Twice the square of the first number increased by the square of the second number is 9
Now, Let The first number = F
And The second number = S
So , According to question
F² - S² = 3 .......A
2 F² - S² = 9 ........B
Now, solving the equations
( 2 F² - S² ) - ( F² - S² ) = 9 - 3
Or, ( 2 F² - F² ) + ( S² - S² ) = 6
Or, F² + 0 = 6
∴ F = [tex]\sqrt{6}[/tex]
Putting the value of F in eq A
So, ( [tex]\sqrt{6}[/tex] )² - S² = 3
Or, 6 - 3 = S²
Or, S² = 3
∴ S = [tex]\sqrt{3}[/tex]
So, The number are [tex]\sqrt{6}[/tex] , [tex]\sqrt{6}[/tex]
Hence The number are [tex]\sqrt{6}[/tex] and [tex]\sqrt{6}[/tex] . Answer
