Photo AI
State the range of values of x for which the binomial expansion of $$ \sqrt{1 - \frac{x}{4}} $$ is valid - AQA - A-Level Maths: Pure - Question 1 - 2022 - Paper 3
Question 1
State the range of values of x for which the binomial expansion of $$ \sqrt{1 - \frac{x}{4}} $$ is valid. Circle your answer. |x| < \frac{1}{4} |x| < 1 |x| < 2 |x... show full transcript
Worked Solution & Example Answer:State the range of values of x for which the binomial expansion of $$ \sqrt{1 - \frac{x}{4}} $$ is valid - AQA - A-Level Maths: Pure - Question 1 - 2022 - Paper 3
Step 1
Determine the valid range for |x|
Answer
For the binomial expansion to be valid, the expression inside the square root must be non-negative. This requires:
Solving this inequality:
or equivalently,
Thus, multiplying both sides by 4, we get:
Also, since we are dealing with absolute values, we have:
This is the valid range of values for x for which the binomial expansion is valid.