Question

If 2x-5y =16 and xy=-1 then find the value of 4²x + 25 y²​

Answer 1

Correct Question:

• If 2x - 5y = 16 and xy = -1 then find the value of 4x² + 25y²

Solution:

Given That:

→ 2x - 5y = 16 — (i)

→ xy = -1

Squaring both sides of equation (i), we get:

→ (2x - 5y)² = 16²

Using identity (a - b)² = a² - 2ab + b², we get:

→ (2x)² + (5y)² - 2 × (2x) × (5y) = 256

→ 4x² + 25y² - 20xy = 256

Substituting the value of xy, we get:

→ 4x² + 25y² + 20 = 256

→ 4x² + 25y² = 256 - 20

→ 4x² + 25y² = 236

★ Which is our required answer.

Additional Information:

Algebraic Identities.

• (a + b)² = a² + 2ab + b²
• (a - b)² = a² - 2ab + b²
• (a + b)² + (a - b)² = 2(a² + b²)
• (a + b)² - (a - b)² = 4ab
• 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
• (a + b + c)² = a² + b² + c² + 2ab + 2bc + 2ac