Question

find the value of a and b if​

Answer 1

Solution

Given :-

• (7 + 3√5)/(3 + √5) - (7 - 3√5)/(3 - √5) = a + b√5

Find :-

• Value of a & b

Explanation

First we rationalize denominator of part (1).

= (7 + 3√5)/(3 + √5)

For Rationalize denominator , multiply by (3 - √5) Numerator & Denominator

= (7 + 3√5)(3 - √5)/(3 + √5)(3 - √5)

Using Formula,

★ ( a + b)(a - b) = (a² - b²)

★(a + b)(c + d) = ( ac + ad + bc + bd )

So,

= ( 21 - 7√5 + 9√5 - 15)/(3² - √5²)

= ( 6 + 2√5)/(9 - 5)

= 2( 3 + √5)/4

= (3 + √5)/2

Now, Rationalize denominator of part (2)

= 7 - 3√5)/(3 - √5)

For, rationalization Multiply by (3 + √5) in numerator & denominator

= (7 - 3√5)(3 + √5)/(3 - √5)(3 + √5)

= (21 + 7√5 - 9√5 - 15 )/( 3² - √5²)

= ( 6 - 2√5)/(9 - 5)

= 2(3 - √5)/4

= (3 - √5)/2

So, Take all parts

==> (3 + √5)/2 - (3 - √5)/2 = a + b√5

==> ( 3 + √5 - 3 + √5)/2 = a + b√5

==> ( 2√5) = a + b√5

Or,

==> 0 + 2√5 = a + b√5

Take comparison both side,

==> a = 0

And

==> b = 2

Hence

• Value of a = 0
• Value of b = 2

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