If x + y = 10 and 1/x + 1/y = 12/5, then x³ + y³ = ?

M4maths Previous Puzzles

16 Jun 2022 Algebra

If x + y = 10 and 1/x + 1/y = 12/5, then x³ + y³ = ?

OPtion

1) 587
2) 785
3) 578
4) 857
5) 685
6) 875
7) 758
8) 658
9) 865
10) None of these

Solution

Given, x+y=10
1/x + 1/y = 12/5
⇒ (x+y) / xy = 12/5
10/xy = 12/5
xy = 25/6
Now, x³ + y³ = (x + y)(x² − xy + y²)
.' (x+y)² = 10²
x² + y² + 2xy = 100
⇒ x² + y² = 100 - 2xy
.'. x³ + y³ = 10*(100 - 2xy − xy) = 10*[100 - 3*(25/6)] = 875

Correct Option: 6 Best Solution (0)