Question

If x+y=underroot11and x^2+y^2=5then find the value of xy

Answer 1

Answer:

xy = 3

Step-by-step explanation:

x + y = √11

x² + y² = 5

xy = ?

We know that, (x+y)² = x² + y² + 2xy

Putting the values,

=> (√11)² = 5 + 2xy

=> 11 = 5 + 2xy

=> 6 = 2xy

=> xy = 6/2

=> xy = 3

______________________

Verification :

(√11)² = 5 + (2)(3)

=> 11 = 5 + 6

=> 11 = 11

Hence, out answer is correct. Therefore, the value of xy is 3

Answer 2

Given :

$x + y = \sqrt{11}$

${x}^{2} + {y}^{2} = 5$

To find :

The value of xy

Solution :

$x + y = \sqrt{11}$

On Squaring both sides,

$\implies {(x + y)}^{2} = {( \sqrt{11} )}^{2}$

$\implies {x}^{2} + {y}^{2} + 2xy = 11$

$\implies 5 + 2xy = 11$

$\implies 2xy = 11 - 5$

$\implies xy = \dfrac{6}{2}$

$\implies xy = 2$

Identity used :

${(a + b)}^{2} = {a}^{2} + {b}^{2} + 2ab$