Question

if x+y =13 and xy=25/4 then find the value of x-y.

Answer 1

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Answer 2

Answer:

The value of $x-y=-12$

Step-by-step explanation:

Given : $x+y=13$ and $xy=\frac{25}{4}$

To find : The value of x-y ?

Solution :

Let $x+y=13$ ......(1)

$xy=\frac{25}{4}$ ......(2)

Substitute the value of x from (1) and put in (2),

$(13-y)y=\frac{25}{4}$

$13y-y^2=\frac{25}{4}$

$y^2-13y+\frac{25}{4}=0$

$4y^2-52y+25=0$

$(y-0.5)(y-12.5)=0$

$y=0.5,12.5$

Substitute in (1),

When y=0.5, $x+0.5=13$

$x=13-0.5=12.5$

When y=12.5, $x+12.5=13$

$x=13-12.5=0.5$

Therefore, The values are (0.5,12.5) and (12.5,0.5).

Now, Substitute in $x-y$

When, x=0.5 and y=12.5

$x-y=0.5-12.5=-12$

When, x=12.5 and y=0.5

$x-y=12.5-0.5=-12$