Question

prove that 5+2root7 is a rational number....... please do not write any spam

Answer 1

Hi Friend !!

Here is ur answer ,,,


Lets assume that 5+2√7 is rational

Its in the form of p/q where p,q are integers.


5+2√7 = p/q


5 = p/q - 2√7

5² = (p/q-2√7)²

25 = p²/q² - 2(p/q)(2√7) + 4(7)

25 - 28 = p²/q² - 4√7p/q

4√7 p/q = p²/q² + 3

4√7p/q = p²+3q²/q²

√7 = p² + 3q²/ q² ( q/4p)


√7 = p²+3q²/4pq

If p,q are integers then p²+3q²/4pq is rational number.

Then √7 also a rational number.

But it contradicts the fact that √7 is irrational

So, our assumption is wrong. And 5+2√7 is irrational.

....HENCE PROVE...

Hope it helps u
(-:

Answer 2

Answer:

Step-by-step explanation:

Lets assume that 5+2√7 is rational

Its in the form of p/q where p,q are integers.

5+2√7 = p/q

5 = p/q - 2√7

5² = (p/q-2√7)²

25 = p²/q² - 2(p/q)(2√7) + 4(7)

25 - 28 = p²/q² - 4√7p/q

4√7 p/q = p²/q² + 3

4√7p/q = p²+3q²/q²

√7 = p² + 3q²/ q² ( q/4p)

√7 = p²+3q²/4pq

If p,q are integers then p²+3q²/4pq is rational number.

Then √7 also a rational number.

But it contradicts the fact that √7 is irrational

So, our assumption is wrong. And 5+2√7 is irrational.

....HENCE PROVE...