The value of P² + Q² + P · Q including elimination of <em>radical</em> denominators is equal to 13.
<h3>How to find the value of a expression including elimination of radical in denominators</h3>
Herein we have two <em>irrational</em> terms whose denominators are <em>radical</em> expressions, which can be treated by algebraic handling and properties for radical expressions:
P = (√2 + 1) / (√2 - 1)
P = [(√2 + 1) / (√2 - 1)] · [(√2 + 1) / (√2 + 1)]
P = (√2 + 1)² / (2 - 1)
P = (√2 + 1)²
P = 2 + 2√2 + 1
P = 3 + 2√2
Q = (√2 - 1) / (√2 + 1)
Q = [(√2 - 1) / (√2 + 1)] · [(√2 - 1) / (√2 - 1)]
Q = (√2 - 1)²
Q = 2 - 2√2 + 1
Q = 3 - 2√2
Then, the value of P² + Q² + P · Q is:
M = (3 + 2√2)² + (3 - 2√2)² + (3 + 2√2) · (3 - 2√2)
M = 9 + 12√2 + 8 + 9 - 12√2 - 8 + 3 - 8
M = 9 + 8 + 9 - 8 + 3 - 8
M = 21 - 8
M = 13
The value of P² + Q² + P · Q including elimination of <em>radical</em> denominators is equal to 13.
<h3>Remark</h3>
The statement is poorly formatted and reports typing mistakes, correct form is presented below:
<em>If P = (√2 + 1) / (√2 - 1) and Q = (√2 - 1) / (√2 + 1), then find P² + Q² + P · Q.</em>
To learn more on radical equations: brainly.com/question/9370639
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