Question

If X+y=12 and xy=35 , find (x-y)²​

Answer 1

EXPLANATION.

⇒ x + y = 12. - - - - - (1).

⇒ xy = 35. - - - - - (2).

As we know that,

Formula of :

⇒ (x - y)² = (x + y)² - 4xy.

Put the values in the equation, we get.

⇒ (x - y)² = (12)² - 4(35).

⇒ (x - y)² = 144 - 140.

⇒ (x - y)² = 4.

Answer 2

Method -1:

${ \boxed{\boxed{\begin{array}{cc} \bf \: given \\ \\ \rm \to \:x + y = 12 \\ \sf \: and \\ \rm \to \: xy = 35 \: \: \: \: \: \: \\ \\ \sf \: we \: have \: to \: find \: \\ \\ \rm \to value \: of \: {(x - y)}^{2} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \\ \bf \: we \: know \: that \\ \\ \rm( {x - y)}^{2} = {(x + y)}^{2} - 4xy \\ = {(12)}^{2} - 4 \times 35 \\ = 144 - 140 \\ = 4 \\ \\ \rm \therefore {(x - y) }^{2} = 4\end{array}}}}$

Method -2:

${ \boxed{ \boxed{ \begin{array}{cc}\rm \: we \: know \: that \\ \\ \rm \: 4xy = {(x + y)}^{2} - {(x - y)}^{2} \\ \\ \rm = > 4 \times 35 = ({12)}^{2} - {(x - y)}^{2} \\ \\ = > \rm {(x - y)}^{2} = {(12)}^{2} - 4 \times 35 \\ \\ = 144 - 140 \\ \\ = 4 \\ \\ \therefore \rm {(x - y)}^{2} = 4\end{array}}}}$