CAT 2023 Slot 1 Solved Paper

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Question : 47 of 66

Marks: +1, -0

If

{√{5 x+9}}+{√{5 x-9}}=3(2+{√{2}})

, then

{√{10 x+9}}

is equal to

$3 {√{31}}$
$4{√{5}}$
$3 {√{7}}$
$2{√{7}}$

Solution:

Given,

{√{5 x+9}}+{√{5 x-9}}=3(2+{√{2}})

⇒

{√{5 x+9}}+{√{5 x-9}}=6+3 {√{2}}

⇒

{√{5 x+9}}+{√{5 x-9}}={√{36}}+{√{18}}

Comparing the L.H.S. and R.H.S.
⇒

5 x+9=36⇒5 x=27

⇒

x=\;{27}/{5}

(can be verified using the second term as well).

⇒ {√{10 x+9}}=√{ (10 × \;{27}/{5}) +9}={√{63}}=3 {√{7}}

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