KVPY SX SB Exam 2015 Question Paper

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Question : 81 of 120

Marks: +1, -0

Part – II

MATHEMATICS

Let

x = ( √50 + 7)^{1\/3}- (√ 50 - 7)^{1\/3}

. Then -

x = 2
x = 3
x is a rational number, but not an integer
x is an irrational number

Solution:

x = ( √50 + 7)^{1\/3}- (√ 50 - 7)^{1\/3}

x^3 = ( √50 + 7) - (√ 50 - 7)-3 ( √50 + 7) (√ 50 - 7) ( ( √50 + 7)^{1\/3}- (√ 50 - 7)^{1\/3} )

x^3 = 14- 3 (1) (x)

x^3 = 14 - 3x

x^3 + 3x - 14 = 0

x = 2

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