SSC CGL Model Paper 14

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Question : 61 of 100

Marks: +1, -0

For what value of k, the expression

x^ 6-1 8 x ^3 +k

will be a perfect square ?

-9
-81
+9
+81

Solution:

Expression

= x^ 6 - 18x^3 + k

= (x 3)^2 - 2 ×x^ 3 × 9 + k

...(i)
On comparing Eq. (i) from

a^2 + 2 ab + b^2 = (a + b)^2

,

2a b =2 × x^ 3 × 9

⇒ a = x ^3

and

b = 9

∴k = b ^2 = (9 )^2 = 81

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