Question

If (x + y) = 11 and xy = 2 then the value of x power 2 + y power 2 =?

Answer 1

Refer to the attachment provided.

Answer 2

Answer :- x² + y² = 117

Given :-

◉ x + y = 11

◉ xy = 2

To Find :-

◉ x² + y² = ?

Solution :-

Given,

⇒ x + y = 11

Square both sides,

⇒ (x + y)² = (11)²

⇒ x² + y² + 2xy = 121 [∵ (a + b)² = a² + b² + 2ab]

⇒ x² + y² + 2×2 = 121 [ given, xy = 2]

⇒ x² + y² = 121 - 4

⇒ x² + y² = 117

∴ Value of x² + y² is 117

Some Formulae :-

◉ (a - b)² = a² + b² - 2ab

◉ (a + b)³ = a³ + b³ + 3ab(a + b)

◉ (a - b)³ = a³ - b³ - 3ab(a - b)

◉ a³ + b³ = (a + b)(a² - ab + b²)

◉ a³ - b³ = (a - b)(a² + ab + b²)