Prove that 3+2 √5 is an irrational number
harmeetkaurrana642:
dubra post karo question
ok
Let take that 3 + 2√5 is a rational number.
So we can write this number as
3 + 2√5 = a/b
Here a and b are two co prime number and b is not equal to 0
Subtract 3 both sides we get
2√5 = a/b – 3
2√5 = (a-3b)/b
Now divide by 2 we get
√5 = (a-3b)/2b
Here a and b are integer so (a-3b)/2b is a rational number so √5 should be a rational number But √5 is a irrational number so it contradict the fact
Hence result is 3 + 2√5 is a irrational number
So we can write this number as
3 + 2√5 = a/b
Here a and b are two co prime number and b is not equal to 0
Subtract 3 both sides we get
2√5 = a/b – 3
2√5 = (a-3b)/b
Now divide by 2 we get
√5 = (a-3b)/2b
Here a and b are integer so (a-3b)/2b is a rational number so √5 should be a rational number But √5 is a irrational number so it contradict the fact
Hence result is 3 + 2√5 is a irrational number
ye lo
thank you
sooo much
♥️♥️♥️
aap questions kese post karte ho yrr aap ke qustion ka answer he send nhi hotta hai
can we talk later
okkh
Answers
Answered by
5
Given 3+2√5
To prove:3+2√5 is an rational number
proof:
Let us assume that 3+2√5 is a rational number
So it can be written in the form a/b
Here a and b are coprime numbers and b=0
Solving 3+2√5=a/b we get,
=> 2√5=a/b-3
=> 2√5=(a-3b)/b
=>√5 =(a-3b) /2b
This shows (a-3b)/2b is a rational number.But we know that but √5 is an irrational number.
So it contradictsour assumption.
Our assumption of 3+2√5 is a rational number is incorrect.
3+2√5 is an irrational number
Hence proved
Similar questions