Question

please help solve this please​

Answer 1

6

Step-by-step explanation:

m= 4/(3- √5)

m = 4× (3+√5)/4

Rationalizing denominator, (3- √5)

m= 3+√5 ............(1)

Now, m+4/m = (3+√5) + 4/ (3+√5)

Rationalizing denominator, (3 + √5)

= (3+√5) + 4×(3-√5)/ 4

= 3+ √5 + 3- √5

= 6

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Answer 2

Answer:

6

Step-by-step explanation:

$given \\ \\ m = \frac{4}{3 - \sqrt{5} } \\ \\ m = 4 \times \frac{1}{(3 - \sqrt{5}) } \\ \\ m = 4 \times ( \frac{1}{(3 - \sqrt{5} )} \times \frac{(3 + \sqrt{5} )}{(3 + \sqrt{5} )} ) \\ \\ m = 4 \times \frac{(3 + \sqrt{5} )}{( {3}^{2} - {( \sqrt{5}) }^{2}) } \\ \\ m = \frac{4(3 + \sqrt{5} )}{4} \\ \\ m = 3 + \sqrt{5} \\ \\ now \\ \\ m + \frac{4}{m} \\ \\ = (3 + \sqrt{5} ) + \frac{4}{ \frac{4}{(3 - \sqrt{5} )} } \\ \\ = 3 + \sqrt{5} + 3 - \sqrt{5} \\ \\ = 6$

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