1.

If x + y = 4 and x3 + y3 = 12, then the value of x4 + y4 = ?1. 146/92. 146/33. 146/54. 146/7

Answer» Correct Answer - Option 1 : 146/9

Given:

x + y = 4

x3 + y3 = 12

Formula Used:

x2 + y2 = (x + y)2 – 2xy

x3 + y3 = (x + y) (x2 – xy + y2)

x4 + x4 = (x2 + y2)2 – 2x2y2

Calculation:

x3 + y3 = (x + y) (x2 – xy + y2)

⇒ 12 = 4 × (x2 – xy + y2)

⇒ x2 + y2 = 3 + xy

⇒ (x + y)2 – 2xy = 3 + xy

⇒ 42 – 3 = 3xy
⇒ xy = (16 – 3)/3

⇒ xy = 13/3

x4 + x4 = (x2 + y2)2 – 2x2y2

⇒ (3 + xy)2 – 2 × (13/3)2

⇒ [3 + (13/3)]2 – 2 × (169/9)

⇒ [(9 + 13)/9]2 – 338/9

⇒ (484/9) – 338/9

⇒ (484 – 338)/9

⇒ 146/9

∴ The value of x4 + y4 is 146/9.


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