Question

if y+1/2y=4 then y²+1/4y²​

Answer 1

Given:-

• y + 1/(2y) = 4

To find:-

• y² + 1/(4y²)

Answer:-

Given that,

y + 1/(2y) = 4

Squaring both sides,

→ {y + 1/(2y)}² = 4²

• Now we will apply (a + b)² = a² + b² + 2ab with a = y and b = 1/(2y)

→ y² + {1/(2y)}² + {2 * y * 1/(2y)} = 16

→ y² + 1/(4y²) + 1 = 16

→ y² + 1/(4y²) = 16 - 1

→ y² + 1/(4y²) = 15 Ans

Extra knowledge:-

• (a + b)² = a² + b² + 2ab
• (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 + b² - ab)
• a³ - b³ = (a - b)(a² + b² + ab)
• (a + b + c)² = a² + b² + c² + 2(ab + bc + ca)
• a³ + b³ + c³ - 3abc = (a + b + c)(a² + b² + c² - ab - bc - ca)