Question

If
then find value of
xy=6 and x+y=10
x^2+y^2

​

Answer 1

x² + y² = 88 .

Given :-

• xy = 6
• x + y = 10

To Find :-

• x² + y² = ?

Solution :-

As we know that,

(a + b)² = a² + 2ab + b²

A/Q, (x + y)² = x² + 2xy + y²

=> (10)² = x² + y² + 2(6)

=> 100 = x² + y² + 12

=> x² + y² = 100 - 12

=> x² + y² = 88

Thus, the value of x² + y² is 88.

Answer 2

Given :-

• xy = 6
• x + y = 10

To find :-

• x² + y²

Solution :-

As we know that

→ (a + b)² = a² + b² + 2ab {Apply identity}

→ (x + y)² = x² + y² + 2xy

→ (10)² = x² + y² + 2 × 6

→ 100 = x² + y² + 12

→ x² + y² = 100 - 12

→ x² + y² = 88

Hence,

• x² + y² = 88

Some Identities

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