Question

Find the value a and b if √2－1÷√2＋1 -√2＋1÷√2－1=a+√2b

Answer 1

Answer:

On rationalising

(√2-1) × √2-1. => 3-2√2

√2+1. √2-1. 1

similarly second expression = 3+2√2

3-2√2 -(3+2√2)= a+b√2

-4√2 = a+b√2

a=0

b= -4

Answer 2

Answer:

a=0, b= -4

Step-by-step explanation:

√2－1÷√2＋1 -√2＋1÷√2－1=a+√2b, a, b =?

Use of formula:

• (a+b)(a-b)=a²-b²

Rationalizing left side of equation:

• (√2- 1)/(√2+1) - (√2＋1)/(√2－1)=
• (√2- 1)(√2- 1)/(√2- 1)(√2+ 1)  -  (√2＋1) (√2＋1)/ (√2＋1)(√2－1)=
• (√2- 1)²/(2-1) - (√2＋1)²/(2-1)=
• (√2- 1)²+(√2＋1)²=
• (√2-1+√2+1)(√2-1-√2-1)=
• 2√2*(-2)= - 4√2

Now comparing left and right sides of equation:

• a+√2b= - 4√2
• a=0, b= -4

Answer: a=0 and b= -4