In the real number system, the equation \sqrt{x+3-4\sqrt{x-1} +\sqrt{x+8-6\sqrt{x-1}=1 has

Correct Answer is : infinitely many solutions

exactly four distinct solutions

KVPY SX SB Exam 2012 Question Paper

Question : 2 of 120

Marks: +1, -0

In the real number system, the equation

√{x+3-4√{x-1}}

+√{x+8-6√{x-1}}=1

has

Solution:

√{x+3-4√{x-1}}

+√{x+8-6√{x-1}}=1;x ≥ 1

√{(x-1)-2×2√{x-1}+4}

+√{(x-1)-6√{x-1}+9}=1

|√{x-1}-2|

+|√{x-1}-3|=1

Case - I

√{x-1}-2+√{x-1}-3=1

(x ≥ 10)

2√{x-1}=6

x=10

Case -II

√{x-1}-2-√{x-1}+3=1

(5 ≤ x ≤ 10)
Case -III

-√{x-1}-2-√{x-1}+3=1

(1 ≤ x ≤ 5)

2√{x-1}=4

x = 5

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