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Root2+root3/3root2-2root3 = a-broot6. put values of a and b?
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Root2+root3/3root2-2root3 = a-broot6. put values of a and b?
Given Expression
To simplify the expression (√2 + √3) / (3√2 - 2√3), we will multiply the numerator and denominator by the conjugate of the denominator.
Step 1: Multiply by Conjugate
The conjugate of the denominator (3√2 - 2√3) is (3√2 + 2√3). We multiply both the numerator and denominator:
- Numerator: (√2 + √3)(3√2 + 2√3)
- Denominator: (3√2 - 2√3)(3√2 + 2√3)
Step 2: Simplify Denominator
Using the difference of squares formula:
- Denominator = (3√2)² - (2√3)²
- Denominator = 18 - 12 = 6
Step 3: Simplify Numerator
Now, we simplify the numerator:
- (√2 + √3)(3√2 + 2√3) = 3√2 * √2 + 2√3 * √2 + 3√2 * √3 + 2√3 * √3
- = 3 * 2 + 2√6 + 3√6 + 2 * 3
- = 6 + 5√6 + 6
- = 12 + 5√6
Step 4: Final Expression
Now, we have:
(12 + 5√6) / 6
Breaking it down:
- = 2 + (5/6)√6
Comparison with a - b√6
In the form a - b√6, we have:
- a = 2
- b = -5/6
Final Values
- a = 2
- b = -5/6
To simplify the expression (√2 + √3) / (3√2 - 2√3), we will multiply the numerator and denominator by the conjugate of the denominator.
Step 1: Multiply by Conjugate
The conjugate of the denominator (3√2 - 2√3) is (3√2 + 2√3). We multiply both the numerator and denominator:
- Numerator: (√2 + √3)(3√2 + 2√3)
- Denominator: (3√2 - 2√3)(3√2 + 2√3)
Step 2: Simplify Denominator
Using the difference of squares formula:
- Denominator = (3√2)² - (2√3)²
- Denominator = 18 - 12 = 6
Step 3: Simplify Numerator
Now, we simplify the numerator:
- (√2 + √3)(3√2 + 2√3) = 3√2 * √2 + 2√3 * √2 + 3√2 * √3 + 2√3 * √3
- = 3 * 2 + 2√6 + 3√6 + 2 * 3
- = 6 + 5√6 + 6
- = 12 + 5√6
Step 4: Final Expression
Now, we have:
(12 + 5√6) / 6
Breaking it down:
- = 2 + (5/6)√6
Comparison with a - b√6
In the form a - b√6, we have:
- a = 2
- b = -5/6
Final Values
- a = 2
- b = -5/6
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Root2+root3/3root2-2root3 = a-broot6. put values of a and b?
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Root2+root3/3root2-2root3 = a-broot6. put values of a and b? for UPSC 2025 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about Root2+root3/3root2-2root3 = a-broot6. put values of a and b? covers all topics & solutions for UPSC 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Root2+root3/3root2-2root3 = a-broot6. put values of a and b?.
Root2+root3/3root2-2root3 = a-broot6. put values of a and b? for UPSC 2025 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about Root2+root3/3root2-2root3 = a-broot6. put values of a and b? covers all topics & solutions for UPSC 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Root2+root3/3root2-2root3 = a-broot6. put values of a and b?.
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