Question

$if a = \sqrt{10} + 3 \: \: find \: the \: value \: ofa + \frac{1}a \: \: \: \\ a - \frac{1}{a } \: \: \: \: \: \: \: {a}^{2} - \frac{1}{ {a}^{2} }$


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Answer 1

a = square root 10 + 3
If we square both the terms and subtract each other then we have, 10-9 = 1
When the situation is like the given one, then simple trick is, it’s reciprocal is square root 10 - 3 you can calculate by rationalising denominator in case of 1/a
So if a= square root 10 + 3
Then, 1/a = square root 10 - 3

Now, value of a + 1/a = square root 10 + 3 + square root 10 -3 = 2(sq. Root 10)

Value of a-1/a = 6

Value of (a^2 - 1/a)^2 = (10+ 9 + 6sq.root 10) - ( 10 + 9 - 6 sq. Root 10)
= 12 sq. Root 10

Hope, it will help you