Question

IF P/Q=a then P²+Q²/P²-Q²​

Answer 1

Step-by-step explanation:

$\frac{P}{Q} = a \\ \\ \frac{ {P}^{2} + {Q}^{2} }{P^{2} - Q ^{2} } \\ = \frac{ \frac{P ^{2}}{Q^{2} } + 1}{ \frac{ {P}^{2} }{ {Q}^{2} } - 1} \\ = \frac{ ({ \frac{P}{Q}) }^{2} + 1}{ { (\frac{P}{Q}) }^{2} - 1 } \\ = \frac{ {a}^{2} + 1 }{ {a}^{2} - 1}$

Answer 2

Answer:

The correct answer is : (1 + 2/a² + 1/a⁴) / (1 - 1/a⁴)

Step-by-step explanation:

Given that P/Q=a, we can substitute Q with P/a to get the expression P²+Q²/P²-Q². This gives us P² + (P/a)² / P² - (P/a)².

To simplify this expression, we can use the fact that (P/a)² is equal to P²/a². Substituting this into the expression, we get:

P² + P²/a² / P² - P²/a²

We can then find a common denominator for the numerator and denominator, which is P²a². Factoring out P² from both the numerator and denominator, we get:

P²(1 + 1/a²) / P²(1 - 1/a²)

The P² terms cancel out, leaving us with:

(1 + 1/a²) / (1 - 1/a²)

We can simplify this expression further by multiplying both the numerator and denominator by the conjugate of the denominator, which is (1 + 1/a²):

(1 + 1/a²) / (1 - 1/a²) * (1 + 1/a²) / (1 + 1/a²)

Expanding the numerator using the distributive property, we get:

1 + 2/a² + 1/a⁴

And the denominator simplifies to:

1 - 1/a⁴

Therefore, the final simplified expression is:

(1 + 2/a² + 1/a⁴) / (1 - 1/a⁴)

To learn more about denominator, visit:

https://brainly.in/question/12359747

To learn more about numerator, visit:

https://brainly.in/question/17707270

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