Question

If x+y = 7 and xy=11 what is the value of x-y

Answer 1

Answer:

Given:

• x+y=7

• xy=11

• x-y=?

As we know

• (x+y{)}^2 - (x-y{)}^2 = 4xy(x+y)2−(x−y)2=4xy

Putting the values

• (7{)}^2 - (x-y{)}^2 = 4(11)(7)2−(x−y)2=4(11)

• 49 - (x-y{)}^2 = 4449−(x−y)2=44

• - (x-y{)}^2 = 44 - 49−(x−y)2=44−49

• - (x-y{)}^2 = - 5−(x−y)2=−5

Cancellation of Minus

• (x-y{)}^2 = 5(x−y)2=5

Taking square root both hand sides

\sqrt{(x-y{)}^2} = \sqrt{5}(x−y)2=5

• (x-y) = 5(x−y)=5