The larger number is 5.
Explanation
Lets assume, the larger number is [tex] a [/tex] and the smaller number is [tex] b [/tex]
As the sum of two numbers is 9, so...
[tex] a+b= 9 ...............................(1) [/tex]
Now, the sum of their squares is 41, so....
[tex] a^2 + b^2 = 41 .......................................(2) [/tex]
First, solving equation (1) for [tex] b [/tex]....
[tex] b=9-a [/tex]
Now, plugging this [tex] b=9-a [/tex] into equation (2) , we will get...
[tex] a^2 +(9-a)^2 = 41\\ \\ a^2 +81-18a+a^2 =41 \\ \\ 2a^2-18a+81 =41 \\ \\ 2a^2-18a+40=0\\ \\ 2(a^2 -9a+20)=0\\ \\ a^2 -9a+20=0\\ \\ (a-5)(a-4)=0\\ \\ a=5,4 [/tex]
If [tex] a=5 , [/tex] then [tex] b=9-5=4 [/tex]
So, the larger number is 5.
