Question

find rational number a and b such that 1no. _√2-1/√2-1=a+b√2​

Answer 1

Answer:

a = 1, b = 0

Step-by-step explanation:

√2 - 1/√2 - 1 = a + b√2

Rationalizing the denominator -

= √2 - 1/√2 -1 × √2 + 1/√2 + 1

(√2 + 1)(√2 - 1)/(√2 + 1)(√2 - 1)

= (√2)² - (1)²/(√2)² - (1)²

= 2 - 1/2 - 1

1/1 = a + b√2

1 = a + b√2

∴ a = 1

  b = 0

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Answer 2

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