Question

$<marquee>HELLO$

SØLVE THIS QUESTION ❓

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Answer 1

Answer:

Step-by-step explanation:

= 3-2√5 / 6 - √5

multiply 6 + √5 on both numerator and denometor

= (3 - 2√5) x 6 + √5

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  (6 - √5) x 6  + √5

= 18 + 3√5 - 12√5 -10

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     6² - (√5) ²

= 8 - 9√5

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 36 - 5

= 8 -9√5 / 31

so sub in a+ b√5

a = 8/31  and b = -9/31

Answer 2

Step-by-step explanation:

$Given: \frac{3-2\sqrt{5}}{6-\sqrt{5}} = a + b\sqrt{5}$

$\Rightarrow \frac{3-2\sqrt{5}}{6-\sqrt{5}} * \frac{6+\sqrt{5}}{6+\sqrt{5}} = a + b\sqrt{5}$

$\Rightarrow \frac{(3-2\sqrt{5})(6+\sqrt{5})}{(6-\sqrt{5})(6+\sqrt{5})} = a+b\sqrt{5}$

$\Rightarrow \frac{18+3\sqrt{5}-12\sqrt{5}-10}{(6)^2-(\sqrt{5})^2}$

$\Rightarrow \frac{8-9\sqrt{5}}{31} = a+b\sqrt{5}$

$\Rightarrow \frac{8}{31}+\frac{-9}{31}\sqrt{5}= a+b\sqrt{5}$

On comparing both sides, we get

a = (8/31), b = (-9/31)

Hope it helps!