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3 votes
The sum of two numbers is 9 and the sum of their squares is 41. What is the larger number?

2 Answers

3 votes
5 because 5+4 = 9 and 5^2+4^2= 41
Hope this helps!
User Eponier
by
8.5k points
6 votes

The larger number is 5.

Step-by-step explanation

Lets assume, the larger number is
a and the smaller number is
b

As the sum of two numbers is 9, so...


a+b= 9 ...............................(1)

Now, the sum of their squares is 41, so....


a^2 + b^2 = 41 .......................................(2)

First, solving equation (1) for
b....


b=9-a

Now, plugging this
b=9-a into equation (2) , we will get...


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

If
a=5 , then
b=9-5=4

So, the larger number is 5.

User Charles Harring
by
7.8k points

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