Question

If x+y=12 and xy =14 find x 4 + y 4

Answer 1

★ Given :

• x + y = 12
• xy = 14

★ To find :

• Value of x⁴ + y⁴

★ Solution :

• x + y = 12
• xy = 14

Now take x+y = 12 and square in both sides.

→ (x+y)² = 12²

→ x² + y² +2xy = 144

• Put xy = 14

→ x² + y² +2×14 = 144

→ x² + y² + 28 = 144

→ x² + y² = 144-28

→ x² + y² = 116

Now , find the value of x⁴ + y⁴ .

$\to\sf{x^4+y^4}$

$\to\sf{(x^2)^2+(y^2)^2}$

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

$\to\sf{(x^2+y^2)^2-2x^2y^2}$

• Put values : x² + y² = 116 and xy = 14

$\to\sf{(116)^2-2\times(14)^2}$

$\to\sf{13456-392}$

$\to\sf{13064}$

Therefore, the value of x⁴ + y⁴ is 13064.