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Find the value of a and b if √2+√3/3√2-2√3=a-b√6?
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Find the value of a and b if √2+√3/3√2-2√3=a-b√6?
Given Equation:
√2 + √3 / 3√2 - 2√3 = a - b√6
Solution:
Step 1: Rationalize the denominator
To simplify the given equation, we need to rationalize the denominator by multiplying both the numerator and denominator by the conjugate of the denominator.
Step 2: Rationalize the denominator
(√2 + √3) * (3√2 + 2√3) / (3√2 - 2√3) * (3√2 + 2√3)
Step 3: Simplify the expression
= (3√4 + 2√6 + 3√6 + 6) / (9*2 - 4*3)
= (3*2 + 5√6 + 6) / (18 - 12)
= (6 + 5√6 + 6) / 6
= (12 + 5√6) / 6
= 2 + 5/6√6
Step 4: Compare with the given equation
a = 2
b = 5/6
Therefore, the values of a and b are:
a = 2
b = 5/6
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Find the value of a and b if √2+√3/3√2-2√3=a-b√6?
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Find the value of a and b if √2+√3/3√2-2√3=a-b√6? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about Find the value of a and b if √2+√3/3√2-2√3=a-b√6? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Find the value of a and b if √2+√3/3√2-2√3=a-b√6?.
Find the value of a and b if √2+√3/3√2-2√3=a-b√6? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about Find the value of a and b if √2+√3/3√2-2√3=a-b√6? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Find the value of a and b if √2+√3/3√2-2√3=a-b√6?.
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