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which question is this.........
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Answer:
Given : x+y=13x+y=13 and xy=\frac{25}{4}xy=
4
25
To find : The value of x-y ?
Solution :
Let x+y=13x+y=13 ......(1)
xy=\frac{25}{4}xy=
4
25
......(2)
Substitute the value of x from (1) and put in (2),
(13-y)y=\frac{25}{4}(13−y)y=
4
25
13y-y^2=\frac{25}{4}13y−y
2
=
4
25
y^2-13y+\frac{25}{4}=0y
2
−13y+
4
25
=0
4y^2-52y+25=04y
2
−52y+25=0
(y-0.5)(y-12.5)=0(y−0.5)(y−12.5)=0
y=0.5,12.5y=0.5,12.5
Substitute in (1),
When y=0.5, x+0.5=13x+0.5=13
x=13-0.5=12.5x=13−0.5=12.5
When y=12.5, x+12.5=13x+12.5=13
x=13-12.5=0.5x=13−12.5=0.5
Therefore, The values are (0.5,12.5) and (12.5,0.5).
Now, Substitute in x-yx−y
When, x=0.5 and y=12.5
x-y=0.5-12.5=-12x−y=0.5−12.5=−12
When, x=12.5 and y=0.5
x-y=12.5-0.5=-12x−y=12.5−0.5=−12
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