Simple math question help
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Simple math question help

[From: ] [author: ] [Date: 11-06-27] [Hit: ]
What are the numbers?The numbers are 9 and 52.......
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?

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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.

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x+y=61
x^2+y^2=2785
1
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