Question

14. Find the value of a and b in 3+√7/(3-√7)=a+b√7​

Answer 1

Step-by-step explanation:

on rationalising the denominator of 3+√7/3-√7 ,

we get (3+√7)(3+√7)/(3-√7)(3+√7)

=16+6√7/9-7

=16+6√7/2

=8+3√7=a+b√7

on comparison,

we get ,

a=8

b=3

hope it helps

Answer 2

Answer:

taking LHS multiple and divide by

$3 + \sqrt{7}$

$\frac{3 + \sqrt{7} }{3 - \sqrt{7} } \times \frac{3 + \sqrt{7} }{3 + \sqrt{7} }$

$\frac{(3 + \sqrt{7) ^{2} } }{ {3}^{2} - \sqrt{7 ^{2} } }$

$\frac{9 + 7 + 6 \sqrt{7} }{9 - 7}$

using the identities

$(a + b) {}^{2} = a {}^{2} + b {}^{2} + 2ab$

and

$(a + b)(a - b) = a {}^{2} + b {}^{2}$

we get

$\frac{16 + 6 \sqrt{7} }{2}$

taking 2 common

$\frac{2(8 + 3 \sqrt{7} }{2}$

=

$8 + 3 \sqrt{7}$

Now equate this with RHS

a = 8 & b = 3