NTSE Stage 2 SAT 2019 Exam Question Paper

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Question : 42 of 100

Marks: +1, -0

The value of

√{97×98×99×100+1}

is equal to

9901
9891
9801
9701

Solution:

Let

x=97

∴√{97×98×99×100+1}

=√{x(x+1)(x+2)(x+3)+1}

=√{(x^{2}+3x)(x^{2}+3x+2)+1}

=√{(x^{2}+3x)^{2}+2(x^{2}+3x)+1}

=√{(x^{2}+3x+1)^{2}}[∵a^{2}+2ab+b^{2}=(a+b)^{2}]

=x^2+3x+1

=(97)^2+3×97+1\;\;\;\;[∵ x=97]

=9701

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