Question

Find the values of a and b if 3 −√73 +√7= a−b√7

Answer 1

GIVEN:

3 + √7/3 - √7 = a + b√7

TO FIND:

a , b

SOLUTION:

3 + √7/3 - √7 = a + b√7

Taking LHS & rationalising the denominator

(3 + √7)(3 + √7)/(3 + √7)(3 - √7)

Using

• (a + b)² = a² + 2ab + b²

• (a + b)(a - b) = a² - b²

→ 3² + 6√7 + (√7)²/3² - (√7)²

→ 16 + 6√7/2

Taking common

→ 2(8 + 3√7)/2

→ 8 + 3√7

Now, comparing with RHS

8 + 3√7 = a + b√7

a = 8 , b = 3

( a , b ) = ( 8 , 3 )

$\rule{110}2$