Question

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Answer 1

${\overbrace{\underbrace{\purple{Answer}}}}$.

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➡Given here.

♠ a + b √7 = (3 + √7)/(3 - √7 ).

[ Rationalize of denominator ]

=> a + b√7 = (3+√7)(3+√7)/(3-√7)(3+√7).

=> a+b√7 = (9 + 7+ 6√7 )/( 9-7)

=> a+b√7 = (16+6√7)/(2

=> a+b√7 = 8 +3√7.

[ Compare both side , ]

=> So, we find here .

♠ a = 8

♠ b = 3.

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Answer 2

Question:

• If $\frac{3 + \sqrt{7} }{3 - \sqrt{7} } = a + b \sqrt{7}$, then find the value of a and b.

Answer:

$\large\boxed{\sf{a=8\: ,\:b=3}}$

Step-by-step explanation:

It's given that,

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

Rationalisation of Denominator,

$\sf{= > \dfrac{3 + \sqrt{7} }{3 - \sqrt{7} } \times \frac{3 + \sqrt{7} }{3 + \sqrt{7} } = a + b \sqrt{7} } \\ \\ \sf{ = > \dfrac{{(3 + \sqrt{7} )}^{2} }{ {(3)}^{2} - {( \sqrt{7} )}^{2} } = a + b \sqrt{7} }\\ \\ \sf{ = > \frac{9 + 7 + 6 \sqrt{7} }{9 - 7} = a + b \sqrt{7} }\\ \\ \sf{ = > \frac{16 + 6 \sqrt{7} }{2} = a + b \sqrt{7}} \\ \\ \sf{= > 8 + 3 \sqrt{7} = a + b \sqrt{7} }$

Comparing the coefficient on both sides,

• a = 8
• b = 3