Question

prove that 2+3√5=p/q don't spam give me. right answer​

Answer 1

Answer:

.Rational numbers

Any number which can be expressed in the form \dfrac {p}{q}

q

p

for two integers p,\ qp, q (may or may not be coprimes) such that q\neq0q



=0 are called rational numbers.

E.g.: 2, 7, 5/3, 0, -2/5, 0.333..., etc.

Irrational numbers

Unlike rational numbers, any number which cannot be expressed in the form \dfrac {p}{q}

q

p

for two integers p,\ qp, q (may or may not be coprimes) such that q\neq0q



=0 are called irrational numbers.

E.g.: √2, √3, π, e, etc.

=================================

We're given to prove that 2 - 3√5 is irrational. We prove the statement by the method of contradiction.

We first assume that 2 - 3√5 is a rational number. Let me call it as 'x'. So we have,

x=2-3\sqrt5x=2−3

5

Now we are going to express √5 in terms of x from this equation. So,

\begin{gathered}x=2-3\sqrt5\\\\2-x=3\sqrt5\\\\\dfrac {2-x}{3}=\sqrt5\end{gathered}

x=2−3√5

2−x=3√5

2−x/3=5

. use

Now, consider the final equation. Here the LHS of the equation is rational since x is assumed to be rational, but the RHS, √5, is an irrational number. In this equation we see that √5, being an irrational number, is expressed in fractional form, which is not possible.

So we have arrived at the contradiction, and hence proved that 2 - 3√5 is an irrational number.

#answerwithquality

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Answer 2

Answer:

Explanation:

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