Question

Question:-

${y}^{2} + \frac{1}{ {y}^{2} } \: is \: not \: equal \: to \:$

$a) \frac{{y}^{4} + 1 }{ {y}^{2} } \: \: \: \: \: \: b) |y + \frac{1}{y} | \: \: \: \: c) |y - \frac{1}{y} |^{2} + 2 \\ \\ d) |y + \frac{1}{y} | ^{2} - 2$

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please give correct answers
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Answer 1

Answer:

Option (b)

Step-by-step explanation:

Solution :-

Given that

y²+ (1/y²)

=> [(y²×y²)+1]/y²

=> (y⁴+1)/y² --------(1)

or

It can be written as

=> [(y²)²+1²] /y²

We know that

(a+b)² = a²+2ab+b²

=> a²+b² = (a+b)²-2ab

Now,

y²+(1/y²) becomes

=> [{y+(1/y)}²-2(y)(1/y)]

=> [{y+(1/y)}²-2(y/y)]

=> [{y+(1/y)}²-2(1)]

=> [y+(1/y)]²-2 -------(2)

or

We know that

(a-b)² = a²+b²-2ab

=> a²+b² = (a-b)²+2ab

Now,

y²+(1/y²) becomes

=> [{y-(1/y)}²+2(y)(1/y)]

=> [{y-(1/y)}²+2(y/y)]

=> [{y-(1/y)}²+2(1)]

=> [y-(1/y)]²+2 ---------(3)

So

from (1),(2)&(3)

y²+(1/y²)=(y⁴+1)/y²=|[y+(1/y)]|²-2=|[y-(1/y)]|²+2

So y²+(1/y²) is not equal to | y+(1/y) |