Question

If x + y = 11 and xy = 18 then x - y is:  + 3 or - 3 - 7 or + 7 -8 or + 8 + 11 or - 11​
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Answer 1

Answer:

+7

Step-by-step explanation:

So, X+y = 11 Possiblities = 1 + 10 ,2+9 , 3+8 , 4+7 , 5+6 Extra

Xy = 18 = 3 X 6 , 2 x 9 , 1 x 18

In this 2 x 9 is Common So, X = 9 , y = 2

= x-y = 9-2 = +7

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Answer 2

Given,

$x+y=11$ and $xy=18$

We have to find the value of $x-y$

Here we have to use $(a+b)^{2}$ identity

Formula,

$(a+b)^{2} =a^{2}+b^{2}+2ab$

Here, $a=x$

$b=y$

Substitute given values in the above identity

$(x+y)^{2} =x^{2} +y^{2}+2xy$

$x+y=11,xy=18$

$(11)^{2}=x^{2} +y^{2}+2\times18$

$121=x^{2} +y^{2}+36$

$x^{2} +y^{2} =121-36$

$x^{2} +y^{2}= 85$

Now, we have to use $(a-b)^{2}$ to find the value of $(x-y)$

Formula,

$(a-b)^{2}= a^{2}+b^{2} -2ab$

Now, substitute the given values in the above identity

$(x-y)^{2}= x^{2} +y^{2}-2xy$

$(x-y)^{2}= 85-2\times36$

$(x-y)^{2} = 49$

$x-y=\sqrt{49}$

$x-y=$±$7$.

Therefore, the value of $x-y$ is ±$7$.