Question

If a and b be two rational number find the value of a and b in the following, 3+√7/3-√7 = a+b√7.

Answer 1

Hii friend,

3+✓7/3-✓7 = a+b✓7

we have,

=> 3+✓7/3-✓7 = 3+✓7/3-✓7 × 3+✓7/3+✓7.



=>> (3+✓7)²/(3)² - (✓7)².

We know that,

(A+B)² = A²+B²+2 × A × B and (A+B)(A-B) = A²-B².

Therefore,

=> (3)² + (✓7)² + 2 × 3 × ✓7/ 9 -7

=> 9 + 7 +6✓7/2

=> 16+6✓7/2

=> (16/2 +6✓7/2 )

=> 8+3✓7 = a+b✓7

a = 8 and b = 3.

Hence,

A = 8 and B = 3

HOPE IT WILL HELP YOU..... :-)

Answer 2

Hi there !!

a = 8
b = 3

Method is in the attachment :D