If x³ = 184 + y³ and x = 4 + y, then the value of (x + y)…

If x³ = 184 + y³ and x = 4 + y, then the value of (x + y) is (given that x > 0 and y > 0):

Show answer & explanation

Correct answer: B

Explanation

The correct answer is Option 2 i.e. $2{{\sqrt14}}$ .

x³ = 184 + y³ and x = 4 + y

(4 + y)³= 184 + y³

y³ + 12y² + 48y + 64 = 184 + y³

12y² + 48y + 64 = 184

12y² + 48y - 120 = 0

y² + 4y - 10 = 0

after solving

y = -2 + ${{\sqrt14}}$

x = 4 + y = 4 - 2 + ${{\sqrt14}}$ = 2 + ${{\sqrt14}}$

x + y = $2{{\sqrt14}}$

SSC Selection Post 2024 PYQ — Question 54