SSC CGL 9 Aug 2015 Shift 2 Paper

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Question : 124 of 200

Marks: +1, -0

If x =

√{a∛ {b√{a∛ b}}}

.... ∞ then the value of x is

$(ab^3)^{1/5}$
$∛{a^3b}$
$∛{a^5b}$
$(a^3b)^{1/5}$

Solution:

x =

√{a∛ {b√{a∛ b}}}

.... ∞
On squaring both sides,

x^2

= a

∛ {b√{a∛ b}}

.... ∞
Again on cubing both sides,

x^6

=

a^3b √{a∛b}

... ∞
⇒

x^6

=

a^3 bx

⇒

x^6/x

=

x^5

=

a^3b

∴ x =

(a^3b)^{1/5}

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