Question

if x+y=7 and xy=11 then find the value of x-y​

Answer 1

Given:

• x+y=7

• xy=11

• x-y=?

As we know

• $(x+y{)}^2 - (x-y{)}^2 = 4xy$

Putting the values

• $(7{)}^2 - (x-y{)}^2 = 4(11)$

• $49 - (x-y{)}^2 = 44$

• $- (x-y{)}^2 = 44 - 49$

• $- (x-y{)}^2 = - 5$

Cancellation of Minus

• $(x-y{)}^2 = 5$

Taking square root both hand sides

$\sqrt{(x-y{)}^2} = \sqrt{5}$

• $(x-y) = 5$

Answer 2

if x+y=7 and xy=11 then find the value of x-y

$(x + y) = 7 \: and \: \: xy = 11 \: \\ (x + y) {}^{2} - (x - y) {}^{2} = 4xy \\ = > (7) {}^{2} - (x - y) {}^{2} = 4 \times 11 \\ = > 49 - (x - y) {}^{2} = 44 \\ = > - (x - y) {}^{2} = 44 - 49 \\ = > - (x - y) {}^{2} = - 5 \\ = > (x - y) {}^{2} = 5 \\ = (x - y) = \sqrt{5}$