What is the Rationalising factor of 51/3+5-1/3 find the rationalising factor by prrof
What is the Rationalising factor of 51/3+5-1/3 find the rationalising factor by prrof
phani vemuri , 5 Years ago
Grade 9
Integral Calculus> What is the Rationalising factor of 5 1/3...
2 Answers
Arun
Last Activity: 5 Years ago
Dear student
It can be written as 5^1/3 + 5^-1/3
rationalizing factor is ( 5^2/3 + 5 ^-2/3 – 1) as when multiplied, this convert in to the formula of a^3 + b^3
Vikas TU
Last Activity: 5 Years ago
Dear student
Here is the explanation of above question.
Your question is how to rationalize the above expression.
The above answer gives you the shortest way to rationalize the expression.
For finding rationalizing factor you can use this method. This is somewhat complex .
Take 5^1/3=a & 5^-1/3=b
Now find the lcm if the exponents.
In this case since the denominator is same therefore the LCM is 3
Now a^3=5 & b^3=5^-1
Since a and b are rational therefore a^3-b^3 is also rational
a^3-b^3=(a-b)(a^2+ab+b^2)
Rationalizing factor of a-b=(5^1/3–5^-1/3)
=5^2/3+5^–2/3+5^2/3*5^-2/3
Now just solve the above expression and get the rationalizing factor
Hope this will help
Good Luck
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