Question

If 3+√73− √7 = a+ b√7, find the values of a and b ​

Answer 1

${\purple{\underline{\underline{\large{\mathtt{Correct Question:}}}}}}$

If 3+√7 / 3-√7 = a+b√7 find a and b.

${\purple{\underline{\underline{\large{\mathtt{Answer:}}}}}}$

Given:

• We have been given that 3+√7/3-√7 = a+b√7.

To Find:

• We need to find the values of a and b.

Solution:

We have been given that 3+√7/3-√7 = a+b√7.

Inorder to rationalize this, we need yo multiply by 3+√7 in both numerator and denominator.

=>  (3+√7)² / (3-√7)(3+√7) = a + b√7

=> (9 + 7 + 6√7) / (3² -√7²)   = a + b√7

=> 16+ 6√7 / 9-7 = a + b√7

=> 16+ 6√7 / 2 = a + b√7

=> 2(8 + 3√7) / 2 = a + b√7 [Taking 2 as common]

=> 8 +3√7 = a + b√7

Now, on comparing both sides, we get a = 8 and b = 3.

Therefore, a = 8 and b = 3.

Answer 2

CORRECT QUESTION:

If 3 + √7/3 - √7 = a + b√7, then find a , b

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 )