Question

if X^2+y^2=55 and xy=3 , find the if value of x-y​

Answer 1

Answer:

x-y =. 7

Step-by-step explanation:

x²+y²-2xy = 55-6

(x-y)²=49

x-y=7

Answer 2

Given :

x² + y² = 55

xy = 3

To find : x-y.

Identity to use : (a-b)² = a² - 2ab + b²

Where a = x and b = y.

substituting the values,

(x-y)² = (x)² - [2×(x)×(y)] + (y)²

by rearranging,

(x-y)² = (x)² + (y)² - [2×(x)×(y)]

(x-y)² = x² + y² -2xy

as we know x² + y² = 55 and xy = 3, by substituting the values,

(x-y)² = 55 - 2(3)

(x-y)² = 55 - 6

(x-y)² = 49

(x-y) = √49 [by transposing the power]

(x-y) = 7

Verification :

substituting (x-y) for 7,

(x-y)² = x² + y² - 2xy

(7)² = 55 - 6

49 = 55 - 6

LHS = RHS

Hence verified

Some more identities :

(a+b)² = a² + 2ab + b²

a²-b² = (a+b)(a-b)

(x+a)(x+b) = x² + x(a+b) + (ab)

(a+b+c)² = a² + b² + c² + 2ab + 2bc + 2ca

(a+b)³ = a³ + 3a²b + 3ab² + b³

(a-b)³ = a³ - 3a²b + 3ab² - b³

a³+b³ = (a+b)(a²-ab+b²)

a³-b³ = (a-b)(a²+ab+b²)

a³+b³+c³-3abc = (a+b+c)(a²+b²+c²-ab-bc-ca)

Conditional identity:

if a+b+c = 0,

a³+b³+c³ = 3abc