Question

please solve this clearly... it's urgent ​

Answer 1

Solution

Given:-

• (a + b√5) = (4 + 3√5)/(4 - 3√5)

Find :-

• Value of a & b

Explanation

First , we Rationalize denominator of R.H.S.

==> a + b√5 = (4+3√5)(4-3√5)/(4-3√5)(4+3√5)

Using Formula

★ (a + b)² = a² + b² + 2ab.

★ (a - b)² = a² + b² - 2ab

★(a - b)(a + b) = (a² - b²) .

So, keep all required values

==> a + b√5 = (4+3√5)²/[4² - (3√5)²]

==> a + b√5 = [4² + (3√5)² + 2×4×3√5]/(16 - 45)

==> a + b√5 = [ 16 + 45 + 24√5]/(-29)

==> a + b√5 = - (61 + 24√5)/29

==> a + b√5 = -61/29 - 24√5/29

Now, compare both side .

For, a.

==> a = -61/29 .

For, b

==> b = -24/29

Hence

• Value of a = -61/29
• Value of b = -24/29

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