Answer:
2√6 +2 and 2√6 -2
Explanation:
You want two numbers such that one is 4 more than the other and the sum of their squares is 56.
Setup
Let x represent the smaller number. The the sum of the squares of the two numbers is ...
x² +(x +4)² = 56
Solution
Simplifying the equation, we have ...
2x² +8x +16 = 56
x² +4x = 20 . . . . . . . . . subtract 16, divide by 2
x² +4x +4 = 24 . . . . . . add 4 to complete the square
(x +2)² = 2²·6 . . . . . . . write in terms of squares
x = 2√6 -2 . . . . . . . . positive square root, subtract 6
The two numbers are 2√6 -2 and 2√6 +2.
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Additional comment
Their approximate decimal values are 6.8990 and 2.8990. As you expect, the sum of the squares of the rounded values differs slightly from 56.