Question

If x+y=14 and xy=9 , find the value of (x^2+y^2)​

Answer 1

$\textsf{\large{\underline{Solution}:}}$

Given That:

→ x + y = 14

→ xy = 9

We know that:

→ (a + b)² = a² + 2ab + b²

Therefore:

→ (x + y)² = x² + 2xy + y²

→ 14² = x² + 2xy + y²

→ x² + 2xy + y² = 196

Substituting the value of xy, we get:

→ x² + y² + 2 × 9 = 196

→ x² + y² + 18 = 196

→ x² + y² = 196 - 18

→ x² + y² = 178

★ Which is our required answer.

$\textsf{\large{\underline{More Identities To Know}:}}$

• (a + b)² = a² + 2ab + b²
• (a - b)² = a² - 2ab + b²
• a² - b² = (a + b)(a - b)
• (a + b)³ = a³ + 3ab(a + b) + b³
• (a - b)³ = a³ - 3ab(a - b) - b³
• a³ + b³ = (a + b)(a² - ab + b²)
• a³ - b³ = (a - b)(a² + ab + b²)
• (x + a)(x + b) = x² + (a + b)x + ab
• (x + a)(x - b) = x² + (a - b)x - ab
• (x - a)(x + b) = x² - (a - b)x - ab
• (x - a)(x - b) = x² - (a + b)x + ab