Question

If x + y = 7 and xy = 10, then x – y is
$\left( a \right) \pm 3$
$\left( b \right) \pm 7$
$\left( c \right) \pm 10$
$\left( d \right) \pm 17$

Answer 1

Hint: In this particular question use the common fact that ${\left( {x - y} \right)^2} = {\left( {x + y} \right)^2} - 4xy$ so simply substitute the values in this equation so use these concepts to reach the solution of the question.

Complete step-by-step answer:
Given equation:
x + y = 7................... (1)
xy = 10................ (2)
Now as we know the common fact that,
${\left( {x - y} \right)^2} = {\left( {x + y} \right)^2} - 4xy$
Now substitute the values from equation (1) and (2) in the above equation we have,
 $ \Rightarrow {\left( {x - y} \right)^2} = {\left( 7 \right)^2} - 4\left( {10} \right)$
Now simplify the above equation we have,
$ \Rightarrow {\left( {x - y} \right)^2} = 49 - 40 = 9$
Now take the square root on both sides we have,
$ \Rightarrow \sqrt {{{\left( {x - y} \right)}^2}} = \sqrt 9 $
$ \Rightarrow \left( {x - y} \right) = \pm 3$
Therefore, x – y = 3, or x – y = -3.
So this is the required answer.
Hence option (a) is the correct answer.

Note: Whenever we face such types of questions the key concept we have to remember is that always recall the standard identity which is stated above, then after substituting the values simplify it as above we will get the required answer of (x – y), always recall that the square root of any number is always comes as positive, negative i.e. $\sqrt 4 = \pm 2$.