It's pretty simple, I've just forgotten how to do this type of question and need to remember. Thanks for your help!
Two numbers have a sum of 61. The sum of their squares is 2785.
What are the numbers?
Two numbers have a sum of 61. The sum of their squares is 2785.
What are the numbers?
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Write what you know as equations:
a + b = 61
a^2 + b^2 = 2785
Use equation 1 to express b in terms of a:
b = 61 - a
Substitute the 61 - a for b in equation 2:
a^2 + (61 - a)^2 = 2785
Square the (61 - a) term:
a^2 + (3721 - 122a + a^2) = 2785
Combine like tems:
2a^2 - 122a + 3721 = 2785
Subtract 2785 from both sides:
2a^2 - 122a + 936 = 0
Divide through by 2:
a^2 - 61a + 468 = 0
Factor to:
(a - 9)(a - 52) = 0
The numbers are 9 and 52.
a + b = 61
a^2 + b^2 = 2785
Use equation 1 to express b in terms of a:
b = 61 - a
Substitute the 61 - a for b in equation 2:
a^2 + (61 - a)^2 = 2785
Square the (61 - a) term:
a^2 + (3721 - 122a + a^2) = 2785
Combine like tems:
2a^2 - 122a + 3721 = 2785
Subtract 2785 from both sides:
2a^2 - 122a + 936 = 0
Divide through by 2:
a^2 - 61a + 468 = 0
Factor to:
(a - 9)(a - 52) = 0
The numbers are 9 and 52.
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x+y=61
x^2+y^2=2785
x^2+y^2=2785