crays said:Hi, its me again.
[tex]\left(1 - x\right)^{\frac{1}{5}}[/tex]
show that [tex]31.2^{\frac{1}{5}} \approx \frac{197}{99} [/tex]
how can i know what value should x be ?
crays said:[32(0.975)]^1/5
(2)(1-0.025)^1/5
then let x = 0.025?
Binomial expansion is a mathematical technique that allows us to expand an expression raised to a power into a polynomial. In this case, we can use binomial expansion to expand 31.2^(1/5) into a polynomial and then approximate it to the fraction 197/99.
The first step is to rewrite the expression 31.2^(1/5) as (31.2)^(1/5). Then, we use the binomial expansion formula to expand (31.2)^(1/5) into a polynomial. Finally, we can approximate the polynomial to the fraction 197/99.
Binomial expansion is a powerful tool in mathematics that allows us to approximate complex expressions into simpler ones. In this case, it allows us to solve a seemingly difficult equation involving a fractional exponent with a simple polynomial approximation.
Yes, there are other techniques that can be used to solve this equation, such as logarithms or using a calculator. However, binomial expansion is a more efficient and precise method for approximation.
The approximation using binomial expansion is very accurate, with an error of less than 0.05%. This means that the value of 31.2^(1/5) is very close to 197/99, making it a reliable and efficient method for solving this equation.