Aptitude | Algebra | Question 1

Given two numbers x and y such that 

1. x³ + y³ = 9 

2. x + y = 3

Find the value of x⁴+y⁴      

(A)

2/3

(B)

7

(C)

13

(D)

17

Answer: (D)

Explanation:

x3+y3 = (x + y) × (x2 − xy + y2)

Putting given values of x3+y3 and (x + y)
9 = 3 × ((x+y)2 − 3xy)
  = 3 × (9 − 3xy) 
  = 27 − 9xy

9xy = 18
xy = 2

x4 + y4 = (x2 + y2)2 - 2x2y2
   = (x2 + y2)2 - 2*4 
                                  [Putting value of xy]
   = ((x + y)2 - 2xy)2 - 2*4 
                            [Putting values of (x+y) and xy]
   = (9 - 4)2 - 2*4 
   = 17

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