SSC CGL Model Paper 18

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Question : 61 of 100

Marks: +1, -0

If

x + y =5, x ^3 + y ^3 =35

, then what is the positive difference between x and y ?

0
1
5
6

Solution:

x + y =5, x ^3 + y ^3 =35

⇒

(x + y)^3= ( 5)^3

⇒

x^3 + y ^3 + 3 xy (x + y ) = 125

⇒

35 + 3xy×5 = 125

⇒

15xy=90

∴

xy= 6

(x + y ) ^2 =(5)^2

⇒

x^2 + y^ 2 + 2xy =25

⇒

x ^2 + y^ 2 = 2 5 - 2 × 6 = 2 5 -1 2

⇒

x^ 2 + y^ 2 =13

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

= 1 3 - 2 × 6

⇒

( x -y ) ^2 =1

∴

x - y = 1

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