Question

If :-
x^2 +y^2 =25
x×y = 12
then find the value of X


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Answer 1

 Only positive values are taken

Answer:

4

Explanation:

 x^2 + y^2 = 25

Add 2xy both sides :

⇒ x^2 + y^2 + 2xy = 25 + 2xy

⇒ ( x + y )^2 = 25 + 2(12) = 25 + 24

⇒ ( x + y )^2 = 49

⇒ x + y = 7      ...( 1 )

  Add - 2xy both sides of x^2 + y^2:

⇒ x^2 + y^2 - 2xy = 25 - 2xy

⇒ ( x - y )^2 = 25 - 2( 12 ) = 25 - 24

⇒ x - y = 1            ...( 2 )

       adding ( 1 ) and ( 2 ):

⇒ ( x + y ) + ( x - y ) = 7 + 1

⇒ 2x = 8

⇒ x = 4

  Hence the required value of x is 4.

Answer 2

GIVEN:

• x² + y² = 25
• xy = 12

TO FIND:

• x = ?

SOLUTION:

We know that

a² + b² = ( a + b )² - 2ab

Similarly

→ x² + y² = ( x + y )² - 2xy

→ 25 + 2( 12 ) = ( x + y )²

→ 25 + 24 = ( x + y )²

→ x + y = √49

→ x + y = 7 ---------( 1 )

______________________________

x² + y² = 25

Adding ( - 2xy ) on both sides to equation 1

→ x² + y² - 2xy = 25 - 2xy

→ ( x - y )² = 1

→ x - y = 1 ---------- ( 2 )

Adding both the equations

→ x + y + x - y = 7 + 1

→ 2x = 8

→ x = 8/2

→ x = 4

Hence, x = 4