Question

help me solving this Question....

Answer 1

Answer:

a= -16/103, b= -15/103

Step-by-step explanation:

3+√7/ 3-4√7

By rationalising the denominator,

(3+√7)(3+4√7) / (3-4√7)(3+4√7)

= 9 + 12√7 +3√7+ 7 / 9- 112

= 16+15√7 / -103

=-16/103 - 15√7/103

On comparing with a+b√7, we get

a= -16/103

b= -15/103

Hope it helps!

Answer 2

Answer:

Above image is having step by step solution

Answer of this question is a = - 37/103 & b = - 15/103

1. $\dfrac{3\:+\:\sqrt{7}}{3\:-\:4\sqrt{7}}$

Rationalise numerator and denominator and multiply it with

$(3\:+\:4\sqrt{7})$

Step 1

$\dfrac{3\:+\:\sqrt{7}}{3\:-\:4\sqrt{7}}\times\dfrac{3\:+\:4\sqrt{7}}{3\:+\:4\sqrt{7}}$

Step 2

$\dfrac{(3\:+\:\sqrt{7})(3\:+\:4\sqrt{7})}{(3)^{2}-(4\sqrt{7})^{2}}$

Step 3

Simplification

$\dfrac{9\:+\:12\sqrt{7}\:+\:3\sqrt{7}\:+\:28}{9\:-\:112}$

Step 4

$\dfrac{37\:+\:15\sqrt{7}}{-103}$

Compare LHS & RHS

$\dfrac{37\:+\:15\sqrt{7}}{-103}\: =\: a\:+\:b\sqrt{7}$

Answer

$a\:=\:-\dfrac{37}{103}$

$b\:=\:-\dfrac{15\sqrt{7}}{103}$