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If x = 2 - root 3 then find the value of x square + 1 by x square?
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If x = 2 - root 3 then find the value of x square + 1 by x square?
Given: x = 2 - √3
To find: (x^2 + 1) / x^2
Solution:
Step 1: Calculate x^2
x = 2 - √3
x^2 = (2 - √3)^2
x^2 = 4 - 4√3 + 3
x^2 = 7 - 4√3
Step 2: Find x^2 + 1
x^2 + 1 = 7 - 4√3 + 1
x^2 + 1 = 8 - 4√3
Step 3: Calculate (x^2 + 1) / x^2
(x^2 + 1) / x^2 = (8 - 4√3) / (7 - 4√3)
To rationalize the denominator, multiply both the numerator and denominator by the conjugate of the denominator:
(x^2 + 1) / x^2 = [(8 - 4√3) * (7 + 4√3)] / [(7 - 4√3) * (7 + 4√3)]
(x^2 + 1) / x^2 = (56 - 16√3 + 28√3 - 48) / (49 - 48)
(x^2 + 1) / x^2 = (8√3 + 8) / 1
(x^2 + 1) / x^2 = 8√3 + 8
Therefore, the value of (x^2 + 1) / x^2 when x = 2 - √3 is 8√3 + 8.
To find: (x^2 + 1) / x^2
Solution:
Step 1: Calculate x^2
x = 2 - √3
x^2 = (2 - √3)^2
x^2 = 4 - 4√3 + 3
x^2 = 7 - 4√3
Step 2: Find x^2 + 1
x^2 + 1 = 7 - 4√3 + 1
x^2 + 1 = 8 - 4√3
Step 3: Calculate (x^2 + 1) / x^2
(x^2 + 1) / x^2 = (8 - 4√3) / (7 - 4√3)
To rationalize the denominator, multiply both the numerator and denominator by the conjugate of the denominator:
(x^2 + 1) / x^2 = [(8 - 4√3) * (7 + 4√3)] / [(7 - 4√3) * (7 + 4√3)]
(x^2 + 1) / x^2 = (56 - 16√3 + 28√3 - 48) / (49 - 48)
(x^2 + 1) / x^2 = (8√3 + 8) / 1
(x^2 + 1) / x^2 = 8√3 + 8
Therefore, the value of (x^2 + 1) / x^2 when x = 2 - √3 is 8√3 + 8.
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If x = 2 - root 3 then find the value of x square + 1 by x square?
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If x = 2 - root 3 then find the value of x square + 1 by x 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 - root 3 then find the value of x square + 1 by x square? covers all topics & solutions for Class 9 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If x = 2 - root 3 then find the value of x square + 1 by x square?.
If x = 2 - root 3 then find the value of x square + 1 by x 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 - root 3 then find the value of x square + 1 by x square? covers all topics & solutions for Class 9 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If x = 2 - root 3 then find the value of x square + 1 by x square?.
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