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If X = √2 + 1 by root 2 - 1 and y equal to root 2 minus 1 by root 2 + 1 then find the values of x square + xy + y square?
Most Upvoted Answer
If X = √2 + 1 by root 2 - 1 and y equal to root 2 minus 1 by root 2 + ...
Explanation:
Given:
X = √2 + 1 / √2 - 1
Y = √2 - 1 / √2 + 1
Step 1: Finding the values of x and y
To simplify X and Y, we can rationalize the denominators:
X = (√2 + 1)(√2 + 1) / (√2 - 1)(√2 + 1)
X = (2 + 2√2 + 1) / (2 - 1)
X = 3 + 2√2
Similarly, for Y:
Y = (√2 - 1)(√2 - 1) / (√2 + 1)(√2 - 1)
Y = (2 - 2√2 + 1) / (2 - 1)
Y = 3 - 2√2
Step 2: Finding the value of x^2 + xy + y^2
Now, we need to find:
X^2 + XY + Y^2
= (3 + 2√2)^2 + (3 + 2√2)(3 - 2√2) + (3 - 2√2)^2
= 9 + 12√2 + 8 + 9 - 6 + 4 + 9 - 12√2 + 8
= 30
Therefore, the value of x^2 + xy + y^2 is 30.
Given:
X = √2 + 1 / √2 - 1
Y = √2 - 1 / √2 + 1
Step 1: Finding the values of x and y
To simplify X and Y, we can rationalize the denominators:
X = (√2 + 1)(√2 + 1) / (√2 - 1)(√2 + 1)
X = (2 + 2√2 + 1) / (2 - 1)
X = 3 + 2√2
Similarly, for Y:
Y = (√2 - 1)(√2 - 1) / (√2 + 1)(√2 - 1)
Y = (2 - 2√2 + 1) / (2 - 1)
Y = 3 - 2√2
Step 2: Finding the value of x^2 + xy + y^2
Now, we need to find:
X^2 + XY + Y^2
= (3 + 2√2)^2 + (3 + 2√2)(3 - 2√2) + (3 - 2√2)^2
= 9 + 12√2 + 8 + 9 - 6 + 4 + 9 - 12√2 + 8
= 30
Therefore, the value of x^2 + xy + y^2 is 30.
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If X = √2 + 1 by root 2 - 1 and y equal to root 2 minus 1 by root 2 + 1 then find the values of x square + xy + y square?
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If X = √2 + 1 by root 2 - 1 and y equal to root 2 minus 1 by root 2 + 1 then find the values of x square + xy + y square? for Class 9 2024 is part of Class 9 preparation. The Question and answers have been prepared according to the Class 9 exam syllabus. Information about If X = √2 + 1 by root 2 - 1 and y equal to root 2 minus 1 by root 2 + 1 then find the values of x square + xy + y square? covers all topics & solutions for Class 9 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If X = √2 + 1 by root 2 - 1 and y equal to root 2 minus 1 by root 2 + 1 then find the values of x square + xy + y square?.
If X = √2 + 1 by root 2 - 1 and y equal to root 2 minus 1 by root 2 + 1 then find the values of x square + xy + y square? for Class 9 2024 is part of Class 9 preparation. The Question and answers have been prepared according to the Class 9 exam syllabus. Information about If X = √2 + 1 by root 2 - 1 and y equal to root 2 minus 1 by root 2 + 1 then find the values of x square + xy + y square? covers all topics & solutions for Class 9 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If X = √2 + 1 by root 2 - 1 and y equal to root 2 minus 1 by root 2 + 1 then find the values of x square + xy + y square?.
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