Question

$if \frac{7 + 3 \sqrt{5} }{7 - 3 \sqrt{5} } = \frac{a}{2} + \frac{b \sqrt{5} }{2} \\ find \: a \: and \: b \:$
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Answer 1

Explanation:

$\mathsf{\frac{7+3\sqrt5}{7-3\sqrt5}}$

$\mathsf{=\frac{(7+3\sqrt5)(7+3\sqrt5)}{(7-3\sqrt5)(7+3\sqrt5)}}$

$\mathsf{=\frac{7^2+2(7)(3\sqrt5)+(3\sqrt5)^2}{7^2-(3\sqrt5)^2}}$ [∵ $\mathsf{(a+b)^2=a^2+2ab+b^2,\:(a+b)(a-b)=a^2 - b^2}$]

$\mathsf{=\frac{49+42\sqrt5+45}{49-45}}$

$\mathsf{=\frac{94+42\sqrt5}{4}}$

$\mathsf{=\frac{94}{4}+\frac{42\sqrt5}{4}}$

$\mathsf{=\frac{47}{2}+\frac{21\sqrt5}{2}}$

∴ $\mathsf{\frac{7+3\sqrt5}{7-3\sqrt5}=\frac{a}{2}+\frac{b\sqrt5}{2}}$

$\mathsf{==>\frac{a}{2}+\frac{b\sqrt5}{2}=\frac{47}{2}+\frac{21\sqrt5}{2}}$

∴ $\mathsf{a=47,\:b=21}$

Answer: a = 47, b = 21

I hope this helps. :D

Answer 2

Answer:

a=94. b =42. [100% correct ] , Mark BRAINLIST

Step-by-step explanation:

Please Mark as BRAINLIST answer, If I am right.