(x-y)=5 and xy=36, find the value of x2+y2.
ans-97
Answers
Given:-
x-y = 5 .......................(1)
and
xy = 36......................(2)
To find :-
Values of x and y
Solution :-
From equation 2, We get.
y = 36/x
Putting this value in equation 1 we get....
x - (36/x)= 5 ..........(3)
Multiplying equation 3 by x and rearranging, we get
x² - 5x -36 = 0
Now
x² - 9x + 4x -36 = 0
x(x - 9) + 4 (x - 9)
(x - 9) (x + 4)
x = 9 , 4
Therefore , we got two values of x
hence
If X = 9
then y = 36/9 = 4
And if x = 4
y = 36/4 = 9
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Given:-
x-y = 5 .......................(1)
and
xy = 36......................(2)
To find :-
Values of x and y
Solution :-
From equation 2, We get.
=> y = 36/x
Putting this value in equation 1 ,
=> x - (36/x)= 5 ..........(3)
Multiplying equation 3 by x and rearranging,
=> x² - 5x -36 = 0
Now
=> x² - 9x + 4x -36 = 0
=> x(x - 9) + 4 (x - 9)
=> (x - 9) (x + 4)
=> x = 9 , 4
If X = 9 then y = 36/9 = 4
And if x = 4
=> y = 36/4 = 9
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