Question

if x+y=5 and xy=4 find x-y using suitable identities​

Answer 1

Answer:

(x+y)2 = x2 - 2xy + y2. = x2 + 2xy + y2 - 4xy. = (x+y)2 - 4xy. = 52 - 4 × 4. = 25 - 16 = 9. ∴ x - y = √9. = 3 ...

Answer 2

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Question : If x+y=5 and xy=4 find x-y using suitable identities​.

Answer :  $\pm3$

Step-by-step explanation :

→Using Identities :

$(x-y)^2=(x+y)^2-4xy\\\\=>(x-y)^2=5^2-4(4)[Given]\\\\=>(x-y)^2=25-16\\\\=>(x-y)^2=9\\\\=>(x-y)=\pm3$

→ Using General Procedure :

$Given,(x+y)=5...(1) \\\\xy=4\\\\=>x=\frac{4}{y}$

Now substitute this in (1), we get ,

$(\frac{4}{y}+y )=5$

Now take LCM.

$=>4+y^2=5y\\\\=>y^2-5y+4=0\\\\=>y^2-y-4y+4=0\\\\=>y(y-1)-4(y-1)=0\\\\=>(y-1)(y-4)=0\\\\=>y-1=0,y-4=0\\\\=>y=1,y=4$

If y = 1 ,

x + (1) = 5

=> x = 4

If y = 4,

x + (4) = 5\\

=> x = 1

So the values of x and y be 1,4 or 4,1 respectively.

=> x - y = ( 1 - 4 ) = - 3

or x - y = ( 4 - 1 ) = 3

=> x - y = ± 3

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