Question

if x+y=9 andx^2+y^2=49 then find the value of xy​

Answer 1

Answer:

x y = 16.

Step-by-step explanation:

Given :

x + y = 9 ... ( i )

$\large x^2+y^2=49 \ ...( ii )$

We have to find xy

Using identity here we get

$\large (a+b)^2=a^2+b^2+2ab\\\\\\\large \text{Rewrite as }\\\\\\\large (a+b)^2-(a^2+b^2)=2ab$

Now put the values of ( i ) and  ( ii ) we get

$\large (9)^2-(49)=2xy\\\\\\\large 2xy=81-49\\\\\\\large 2xy=32\\\\\\\large xy=16$

Thus we get answer 16.

Answer 2

Answer :-

$\boxed{ \tt xy = 16 }$

Explanation :-

Given :-

x + y = 9

x² + y² = 49

To find :-

Value of xy

Solution :-

We know that,

(x + y)² = x² + y² + 2xy

It can be written as

⇒ (x + y)² - x² - y² = 2xy

⇒ (x + y)² - (x² + y²) = 2xy

Here x + y = 9 , x² + y² = 49

By substituting the values

⇒ (9)² - (49) = 2xy

⇒ 81 - 49 = 2xy

⇒ 32 = 2xy

⇒ 32/2 = xy

⇒ 16 = xy

⇒ xy = 16

$\Huge{\boxed{ \tt xy = 16 }}$

Verification :-

(x + y)² - (x² + y²) = 2xy

⇒ (9)² - (49) = 2(16)

⇒ 81 - 49 = 32

⇒ 32 = 32

Identity used :-

(x + y)² - (x² + y²) = 2ab