Question

4+root 2 upon 2+2root2=a-root b

Answer 1

Answer:

a = 3 and b=2

Step-by-step explanation:

( 4+√2 )/( 2+√2) = ( 4+√2)( 2-√2) / ( 2+√2)( 2-√2)

= ( 8 - 2√2 - 2) / ( 2² - √2² )

= ( 6 - 2√2 ) / ( 4-2 )

= ( 6 - 2√2 ) / 2 = 3 - √2 = a-√b

.'. a = 3 and b=2

Answer 2

CORRECT QUESTION:

a - √b = 4 + √2/2-√2

ANSWER:

Taking LHS

Rationalize the denominator

(4+√2)(2-√2)/(2+2√2)(2-√2)

Using

(a + b)(a - b) = a² - b²

8-4√2 + 2√2 - 2/2²- 2

6 - 2√2/2

2(3-√2)/2

= 3 - √2

Comparing

With RHS

3 - √2 = a - √b

Hence,

a = 3

b = 2

CONCEPTS USED:

→ Algebraic identities

→ Surds

MORE INFORMATION:

(a + b)(a - b) = a² - b²

(a + b)² = a² + b² + 2ab

(a - b)² = a² + b² - 2ab

a² + b² = (a + b)² - 2ab