Question

. If x-y = 3 and xy = 7 find the value of x2 + y2.​

Answer 1

EXPLANATION.

⇒ x - y = 3. - - - - - (1).

⇒ xy = 7. - - - - - (2).

As we know that,

Formula of :

⇒ (a - b)² = a² + b² - 2ab.

Using this formula in the equation, we get.

⇒ (x - y)² = x² + y² - 2xy.

Put the values in the equation, we get.

⇒ (3)² = x² + y² - 2(7).

⇒ 9 = x² + y² - 14.

⇒ 9 + 14 = x² + y².

⇒ x² + y² = 23.

Answer 2

Given

$\sf \implies{x -y = 3}$

$\sf \implies{xy = 7}$

Formula

$\sf{ = (x-y) = (x²+ {y)}^{2} - 2xy}$

So

$\sf{ = {x}^{2} + {y}^{2} = (x - {y)}^{2} + 2xy}$

$\sf{ = {(3)}^{2} + 2 \times (7)}$

$\sf \implies{9 + (14)}$

$\bf \implies{23}$

Or

Squaring ,

• (x-y)² = (3)²

Explanation

=>>> x²+y²-2xy = (3)²

=>>> x²+y²-2× (7) = (3)²

=>>> x²+y²-2×(7)=9

=>>>x²+y²=9+14

>>>x²+y²=23