Question

09. (a) If 3+ under root 7 upon 3 - under root 7= a + b under root 7 , find the value of a and b.​

Answer 1

Answer :

a=8

b=3

Step by step explanation :

$\frac{3 + \sqrt{7} }{3 - \sqrt{7} } = a + b \sqrt{7}$

$= \frac{3 + \sqrt{7} }{3 - \sqrt{7} } \times \frac{3 - \sqrt{7} }{3 - \sqrt{7} } = a + b \sqrt{7}$

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

$= \frac{9 + 7 + 6 \sqrt{7} }{9 - 7} = a + b \sqrt{7}$

$= \frac{16 + 6 \sqrt{7} }{2} = a + b \sqrt{7}$

$= 8 + 3 \sqrt{7} = a + b \sqrt{7}$