Question

find value of m and n
1) 3+√2/3-√2=m+n√2​

Answer 1

Answer:

Given 3−23+2=m+n2

On rationalizing  the denominator,

3−23+2×3+23+2

=9−29+2+62

=711+62

m=711,n=76 

∴ Value of m= 7

Answer 2

Step-by-step explanation:

Given:-

3+√2/3-√2=m+n√2

To find:-

find value of m and n ?

Solution:-

Given that :

3+√2/3-√2=m+n√2

LHS :-

(3+√2)/(3-√2)

Denominator = 3-√2

Rationalising factor of 3-√2 = 3+√2

On Rationalising the denominator then

=>[(3+√2)/(3-√2)]×[(3+√2)/(3+√2)]

=>[(3+√2)(3+√2)]/[(3-√2)(3+√2)]

=>(3+√2)^2 /(3^2-(√2)^2)

Since (a+b)(a-b)=a^2-b^2

=>(3+√2)^2 / (9-2)

=>(3+√2)^2 / 7

We know that (a+b)^2 = a^2+2ab+b^2

=>[3^2+2(3)(√2)+(√2)^2]/7

=>(9+6√2+2) / 7

=>(11+6√2) / 7

Now

LHS = RHS

=>(11+6√2)/7 = m+n√2

=>(11/7)+(6/7)√2 = m + n √2

On Comparing both sides then

m = 11/7

n = 6/7

Answer:-

The value of m = 11/7

The value of n = 6/7

Used formulae:-

• (a+b)(a-b)=a^2-b^2
• (a+b)^2 = a^2+2ab+b^2
• The product of two irrational numbers is a rational number then the two numbers are called Rationalising factors to each other.
• The Rationalising factor of a+√b is a-√b.