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Prime Factorisation

Q- proove tha...

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Q- proove that root3-root7 is an irrational number. Q-show that there is no positive integer n for which root n-1+root n+1is rational

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Similar questions

Q. Show that there is no positive integer n for which

\sqrt{n - 1} + \sqrt{n + 1}

n

is a positive integer. Select a possible value of

n

\sqrt{n}

is an irrational number.

Q. Consider the quadratic equation

n x^{2} + 7 \sqrt{n} x + n = 0

n

is a positive integer. Which of the following statements are necessarily correct?
I. For any

n

, the roots are distinct.
II. There are infinitely many values of

n

for which both roots are real.
III. The product of the roots is necessarily an integer.

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