50 points
2 questions
1. the number X is 2 more than the number Y. if the sum of squares of X and Y is 34. Find the product of X and Y
2. the difference between two positive numbers is 5 and the sum of their squares is 73. find the product of these numbers.
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Verified answer
Hello users ...solution:-
we know that:
(x² + y²) = (x - y)² + 2xy
Here,
(1.) ..
Given that;
x is 2 more than the number y
=> x - y = 2
And
sum of square of these numbers = 34
=> x² + y² = 34
Now,
product of these numbers
we know that
=> (x² + y²) = (x - y)² + 2xy
=> 2xy = (x² + y² ) - (x - y )²
=> 2xy = 34 - 2² = 34 - 4 = 30
=> xy = 30 / 2 = 15 Answer
(2.) ....
let ,
first number = x
and,
second number = y
Given that;
the difference between two positive numbers is 5
=> x - y = 5
And
the sum of their squares is 73
=> x² + y² = 73
Here,
Product of these numbers
we know that
=> ( x² + y² ) = ( x- y)² + 2xy
=> 2xy = ( x² + y² ) - (x - y)²
=> 2xy = 73 - 5² = 73 - 25 = 48
=> xy = 48 / 2 = 24 Answer
# hope it helps :)
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