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The sum of two numbers is 6 and the sum of their squares is 90. Find the numbers.

User Chihwei
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1 Answer

18 votes
18 votes

Let's set up the variables for the two numbers --> 'a' , 'b'

Now let's set up some equations based on the given information:

  • sum of two numbers is 6 --> a + b = 6
  • sum of their squares is 90 --> a^2 + b^2 = 90

Equations:

  • a + b = 6 -- equation 1
  • a^2 + b^2 = 90 -- equation 2

Solve (equation 1) for b in terms of a

b = a - 6 -- equation 3

(equation 3) into (equation 2)

a^2 + (a - 6)^2 = 90

a^2 + a^2 - 12a + 36 = 90

2a^2 - 12a - 54 = 0

(2a + 6)(a - 9) = 0

a = -3 -- equation 4

a = 9 -- equation 5

(equation 4) into (equation 1)

-3 + b = 6

b = 9 - --- a = -3, b= 9

(equation 5) into ( equation 1)

9 + b = 6

b = -3 - --- a = 9, b= -3

Since the numbers are interchangeable, the two numbers are -3 and 9.

Hope it helps!

User Afsar Ahamad
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