SSC CGL Model Paper 16

© examsiri.com

Question : 62 of 100

Marks: +1, -0

If

x^ 3 - y^ 3 = 81

and

x - y = 3,

thenwhat is the value of

x^ 2 + y ^2

?

18
21
27
36

Solution:

x^ 3 - y^ 3 = 81

(x-y ) ( x^ 2 + y ^2 + xy) = 81

⇒

3 ×(x ^2 + y^ 2 + xy) = 81

⇒

x^ 2 + y ^2 + xy= 27

⇒

x ^2 + y ^2 = 2 7 - xy

...(i)

x - y =3

On squaring both sides,
⇒

x^ 2 + y^ 2 - 2 x y = 9

x ^2 + y^ 2 = 9 + 2xy

...(ii)
From Eqs. (i) and (ii),

2 7 - x y = 9 + 2xy

⇒

3 x y = 1 8

∴

xy=18/3=6

From Eq. (i),

x ^2 + y^ 2 =27 - 6 = 21

© examsiri.com

Go to Question:

Prev Question

Next Question