Question

solve pls it is my tution work ​

Answer 1

Rationalising Factor of a+b=a-b

Following This Rationalise All Denominator.

(10)Rationalising Factor of √3-1=√3+1

(11) Rationalising Factor of 5+√6=5-√6

(12) Rationalising Factor of 7+4√3=7-4√3

Question 10 and 13 are in Attachment.

Q.12

$\frac{5 - \sqrt{6} }{5 + \sqrt{6} } = a - b \sqrt{6} \\ \\ \frac{5 - \sqrt{6} \times 5 - \sqrt{6} }{5 + \sqrt{6} \times 5 - \sqrt{6} } \\ \\ \frac{(5 - \sqrt{6}) {}^{2} }{ {5}^{2} - \sqrt{6} {}^{2} } \\ \\ \frac{ {5}^{2} + \sqrt{6} {}^{2} - 2 \times 5 \times \sqrt{6} }{25 - 6} \\ \\ \frac{25 + 6 - 10 \sqrt{6} }{19} \\ \\ \frac{31 - 10 \sqrt{6} }{19}$

Comparing Both Sides

a=31/19

b=10/19

$a - b \sqrt{6} = \frac{31}{19} - \frac{10}{19} \sqrt{6}$

Identity Used

a²-b²=(a+b)(a-b)

(a+b)²=a²+b²+2ab

(a-b)²=a²+b²-2ab