Question

Prove that the difference and quotient of 3+2√3 and 3-2√3 are irrational .


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Answer 1

Answer:

The difference of (3+2√3) and(3-2√3) is: 3+2√3-3+2√3=4√3 which is irrational.

The quotient of (3+2√3) and(3-2√3) is:

(3+2√3)/(3-2√3)

=(3+2√3)(3+2√3)/(3-2√3)(3+2√3)

=(3+2√3)²/[(3)²-(2√3)²]

={9+2.3.2√3+(2√3)²}/(9-12)

=(9+12√3+12)/(-3)

=(21+12√3)/(-3)

=3(7+4√3)/(-3)

=7+4√3 is an irrational number

= - (7+4√3) is an irrational number

The quotient of (3+2√3) and(3-2√3) is an irrational number.

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Answer 2

Step-by-step explanation:

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