Find the value of A and B from rational equation

1). Find the value of a and b

If  1/ (√5 + √2) = a√5 + b√2

Sol. 1/ (√5 + √2) = a√5 + b√2  …..(1)

Taking L.H.S

 1/ (√5 + √2) = {1/ (√5 + √2)} * {( √5 - √2 ) / (√5 - √2)] = { (√5 - √2) / (5 – 2)} = (√5 - √2) / 3

By equation (1)

Maths ncert solution

(√5/3 - √2/3) =  a√5 + b√2

Compare both side

a = 1/3 b = -1/2

2).  Find the value of a and b

If  1/ (√5 - √2) = a√5 + b√2

Sol. 1/ (√5 - √2) = a√5 + b√2  …(1)

Taking L.H.S

1/ (√5 - √2) = {1/ (√5 - √2)}*{( √5 + √2 ) / (√5 + √2)] = { (√5 + √2) / (5 – 2)} = (√5 + √2) / 3     

By equation (1)

(√5/3 + √2/3) =  a√5 + b√2

Compare both side

a = 1/3 b = 1/2

3).  Find the value of a and b

If  1/ (√5 + √3) = a√5 + b√3

Sol. 1/ (√5 + √3) = a√5 + b√3   ….(1)

Taking L.H.S

1/ (√5 + √3) = {1/ (√5 + √3)} * {( √5 - √3 ) / (√5 - √3)] = { (√5 - √3) / (5 – 3)} = (√5 - √3) / 2

By equation (1)

(√5/2 - √2/2) =  a√5 + b√2

Compare both side

a = 1/2 b = -1/2

4).  Find the value of a and b

If  1/ (√3 + √2) = a√3 - b√2

Sol.  1/ (√3 + √2) = a√3 - b√2 ….(1)

Taking L.H.S

1/ (√3 + √2) = {1/ (√3 + √2)} * {( √3 - √2 ) / (√3 - √2)] = { (√3 - √2) / (3 – 2)} = (√3 - √2)

By equation (1)

(√3 - √2) =  a√3 - b√2

Compare both side

a = 1 b = 1

5).  Find the value of a and b

If  1/ (√5 - √3) = a√5 + b√3

Sol. 1/ (√5 - √3) = a√5 + b√3   ….(1)

Taking L.H.S

1/ (√5 - √3) = {1/ (√5 - √3)} * {( √5 + √3 ) / (√5 + √3)] = { (√5 + √3) / (5 – 3)} = (√5 + √3) / 2

By equation (1)

(√5/2 + √3/2) =  a√5 + b√3

Compare both side

a = 1/2 b = 1/2

6).  Find the value of a and b

If  1/ (√3 - √2) = a√3 + b√2

Sol. 1/ (√3 - √2) = a√3 + b√2    ….(1)

Taking L.H.S

1/ (√3 - √2) = {1/ (√3 - √2)} * {( √3 + √2 ) / (√3 + √2)] = { (√3 - √2) / (3 – 2)} = (√3 - √2)

By equation (1)

(√3 - √2) =  a√3 + b√2

Compare both side

a = 1 b = -1

7).  Find the value of a and b

If  1/ (√7 + 2) = a√7 + b

Sol. 1/ (√7 + 2) = a√7 + b   ….(1)

Taking L.H.S

1/ (√7 + 2) = {1/ (√7 + 2)} * {( √7 - 2 ) / (√7 - 2)] = { (√7 - 2) / (7 – 4)} = (√7 - 2) / 3

By equation (1)

(√7/3 – 2/3) =  a√7 + b

Compare both side

a = 1/3 b = -2/3

8).  Find the value of a and b

If  1/ (√7 - 2) = a√7 + b

Sol. 1/ (√7 - 2) = a√7 + b    ….(1)

Taking L.H.S

1/ (√7 - 2) = {1/ (√7 - 2)} * {( √7 + 2 ) / (√7 + 2)] = { (√7 + 2) / (7 – 4)} = (√7 + 2) / 3

By equation (1)

(√7/3 + 2/3) =  a√7 + b

Compare both side

a = 1/3 b = 2/3

9).  Find the value of a and b

If  1/ (√7 - √6) = a√7 + b√6

Sol. 1/ (√7 - √6) = a√7 + b√6    ….(1)

Taking L.H.S

1/ (√7 - √6) = {1/ (√7 - √6)} * {( √7 + √6 ) / (√7 + √6)] = { (√7 + √6) / (7 – 6)} = (√7 + √6)

By equation (1)

 (√7 + √6) = (a√7 + b√6)

Compare both side

a = 1 b = 1

Note :-

Use conjugate to rationalize numbers.

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Milan Tomic

Hi. I’m Designer of Blog Magic. I’m CEO/Founder of ThemeXpose. I’m Creative Art Director, Web Designer, UI/UX Designer, Interaction Designer, Industrial Designer, Web Developer, Business Enthusiast, StartUp Enthusiast, Speaker, Writer and Photographer. Inspired to make things looks better.

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