Question

11. Ifx+y= 13 and xy=6 1/4, find x - y.​

Answer 1

Answer:

x - y = ±6√3

explanation:

(x + y)² = x² + y² + 2xy

=> (13)² = x² + y² + 2xy

SUBTRACTING '4xy' ON BOTH SIDES.

=> 169 - 61 = x² + y² - 2xy

=> 108 = (x - y)²

=> x - y = ±6√3

Answer 2

Answer:

x+y = 13

xy = 6 1/4

    = 25 / 4

In this question , we will be using the following algebraic identities :

• ( a+b )² = a² + b² + 2ab
• ( a-b )² = a² + b² - 2ab

Now ,

a = x

b = y

Substituting the values ,

( x+y )² = x² + y² + 2xy

( 13 )² = x² + y² + 2 × 25 / 4

169 = x² + y² + 25 / 2

169×2 = 2x² + 2y² + 25

169×2 = 2 ( x² + y² ) + 25

2 gets cancelled on both sides

169 = x² + y² + 25

x² + y² = 169 - 25

x² + y² = 144

now , we use the second identity

( x-y )² = x² + y² + 2xy

We substitute the values again ,

( x-y ) ² = 144 - 25 / 2

( x-y ) ² = ( 288 - 25 ) / 2

           = 263 / 2

x-y = √263 / 2

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