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If X equal to root 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 equal to root 2 + 1 by root 2 - 1 and y equal to root 2 minus 1 b...
Given Information:
X = (root 2 + 1) / (root 2 - 1)
Y = (root 2 - 1) / (root 2 + 1)
Finding x square + xy + y square:
1. Finding the value of x:
X = (root 2 + 1) / (root 2 - 1)
To simplify, we multiply both numerator and denominator by (root 2 + 1):
X = [(root 2 + 1) * (root 2 + 1)] / [(root 2 - 1) * (root 2 + 1)]
X = (2 + 2 * root 2 + 1) / (2 - 1)
X = 3 + 2 * root 2
2. Finding the value of y:
Y = (root 2 - 1) / (root 2 + 1)
To simplify, we multiply both numerator and denominator by (root 2 - 1):
Y = [(root 2 - 1) * (root 2 - 1)] / [(root 2 + 1) * (root 2 - 1)]
Y = (2 - 2 * root 2 + 1) / (2 - 1)
Y = 3 - 2 * root 2
3. Calculating x square + xy + y square:
(x^2) + xy + (y^2)
= (3 + 2 * root 2)^2 + (3 + 2 * root 2)(3 - 2 * root 2) + (3 - 2 * root 2)^2
= 9 + 12 * root 2 + 8 + 9 - 18 + 12 + 9 - 12 * root 2 + 4
= 40
Therefore, x square + xy + y square = 40.
X = (root 2 + 1) / (root 2 - 1)
Y = (root 2 - 1) / (root 2 + 1)
Finding x square + xy + y square:
1. Finding the value of x:
X = (root 2 + 1) / (root 2 - 1)
To simplify, we multiply both numerator and denominator by (root 2 + 1):
X = [(root 2 + 1) * (root 2 + 1)] / [(root 2 - 1) * (root 2 + 1)]
X = (2 + 2 * root 2 + 1) / (2 - 1)
X = 3 + 2 * root 2
2. Finding the value of y:
Y = (root 2 - 1) / (root 2 + 1)
To simplify, we multiply both numerator and denominator by (root 2 - 1):
Y = [(root 2 - 1) * (root 2 - 1)] / [(root 2 + 1) * (root 2 - 1)]
Y = (2 - 2 * root 2 + 1) / (2 - 1)
Y = 3 - 2 * root 2
3. Calculating x square + xy + y square:
(x^2) + xy + (y^2)
= (3 + 2 * root 2)^2 + (3 + 2 * root 2)(3 - 2 * root 2) + (3 - 2 * root 2)^2
= 9 + 12 * root 2 + 8 + 9 - 18 + 12 + 9 - 12 * root 2 + 4
= 40
Therefore, x square + xy + y square = 40.
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If X equal to root 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 equal to root 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 equal to root 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 equal to root 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 equal to root 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 equal to root 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 equal to root 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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