Math, asked by vridhi0310, 11 months ago

if x+y=5 and xy= 4. find the value of x-y,using identities

gujjarankit: 3 is the answer

vridhi0310: solve it

gujjarankit: not able beacuse already two person are giving the answer

vridhi0310: so slove it here

gujjarankit: here i can not provide u the photo of my solution

vridhi0310: no problem

vridhi0310: plzz solve it here

vridhi0310: bcuz ans is 9

gujjarankit: answer is only 9 when it is the square of (×-y)

Answers

Answered by laxmanacharysangoju

Step-by-step explanation:

(x-y)^2=(x+y)^2-4xy

=(5)^2-4(4)

=25-16

x-y=(+ or -) 3

vridhi0310: i am not able to understand

laxmanacharysangoju: I am using here (a-b)^2=a^2+b^2-2ab

laxmanacharysangoju: a^2+b^2=(a-b)^2+2ab

laxmanacharysangoju: (a-b)^2=(a+b)^2-4ab...this is the formula I have been used here

Answered by hukam0685

The value of x-y is ±3.

Given:

x+y=5
xy=4

To find:

Find the value of x-y using identities.

Solution:

Identities to be used:

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

Step 1:

Squaring both sides of x+y=5

$(x+y)^{2} =5^{2} \\ x^{2} +2xy+y^{2} =25$ ...eq1

Step 2:

Add and subtract 4xy

$x^{2} +2xy+y^{2}+4xy-4xy =25$

$x^{2} +2xy-4xy+y^{2} =25-4xy\\ \\ x^{2} -2xy+y^{2} =25-4xy\\\\$

put the value of xy and rewrite LHS as identity

$(x-y)^{2} =25-4\times4\\ \\ (x-y)^{2} =9\\ \\ (x-y)^{2} =3^{2} \\ \\$

taking square root both sides.

$\bf \red{x-y=\pm3}$

Thus,

Value of x-y is ±3.

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