If root 2 + root 3 upon 3 root 2 minus 2 root 3 equals to a minus b root 6 then find the value of a and b
Answers
Given : (√2 + √3)/ (3√2 - 2√3) = a - b√6
To Find : Value of a & b
Solution:
(√2 + √3)/ (3√2 - 2√3) = a - b√6
(√2 + √3)/ (3√2 - 2√3)
Rationalize the denominator
= (√2 + √3) (3√2 +2√3) / (3√2 - 2√3) (3√2 + 2√3)
Solving numerator
(√2 + √3) (3√2 +2√3)
= √2.3√2 + √2.2√3 + √3.3√2 + √3.2√3
= 6 + 2√6 + 3√6 + 6
= 12 + 5√6
Solving denominator using a² - b² = ( a + b)(a - b)
(3√2)² - (2√3)²
= 18 - 12
= 6
(√2 + √3)/ (3√2 - 2√3) = (12 + 5√6 )/6
= 2 + (5/6)√6
= 2 - (-5/6)√6
comparing with
a - b√6
a = 2
b = - 5/6
value of a and b
a = 2
b = - 5/6
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Answer:
Step-by-step explanation:
