Question

If x+y = 11 and xy = 28, find (x-y) using appropriate identities

Answer 1

Answer:

Hi,

so let's begin it's quite easy to understand as well as to do!!

so ATQ,

we need to find the value of x - y,

before this we need to find the value of x² + y²

as,

=> ( x + y )² = x² + y² + 2 × xy

=> ( 11 )² = x² + y² + 2 × 28

=>. 121 = x² + y² + 56

=> x² + y² = 121 - 56 = 65.

[ : . ( a + b )² = a² + b² + 2ab ]

therefore,

the value of x² + y² = 65,

so we can find:

=> ( x - y )² = x² + y² - 2 × xy

=> ( x - y )² = 65 - 2 × 28

=> ( x - y )² = 65 - 56 = 9

[ : . ( a - b )² = a² + b² - 2ab ]

therefore,

=> ( x - y ) = √9 = 3.

hope that it maybe helpful!!