When (1 ax) 2 , where a is a positive constant, is expanded in ascending powers of x, the coefficients of x and x 3 are equal i Find the exact value of a ii When a has this value, obtain the expansion up to and including the term in x 2 , simplifying the coefficients ...

Lets first expand 1 ax2 using the binomial theorem 1 ax2 1 2ax 232a2x2 23 ...

When (1 + ax) 2 , where a is a positive constant, is expanded in ascending powers

Question:

When (1 + ax)⁻², where a is a positive constant, is expanded in ascending powers of x, the coefficients of x and x³ are equal.

i. Find the exact value of a.

ii. When a has this value, obtain the expansion up to and including the term in x², simplifying the coefficients.

Fantastic news! We've Found the answer you've been seeking!

Step by Step Answer:

Related Book For book-img-for-question

Cambridge International AS & A Level Mathematics Pure Mathematics 2 & 3 Coursebook

ISBN: 9781108407199

1st Edition

Authors: Sue Pemberton, Julianne Hughes, Julian Gilbey

See More Books

Question Posted: Apr 05, 2023 11:07 AM

See More Questions

(a) Find the binomial expansion of (1-8x), 1x < in ascending powers of x up to and including the term in x, simplifying each term. (b) Show that, when x = 1 100' (c) Substitute x = the exact value of...
(a) Expand 1 (2-5r)? Given that the binomial expansion of in ascending powers of x, up to and including the term in x, giving each term as a simplified fraction. 1 2 + (b) find the value of the...
Expand 31 (6x) in ascending powers of x up to and including the term in x 3 , simplifying the coefficients.
Q2. (20 pts) Product structure tree of product A is given in the following table: B(2) A C(3) D(3) E(4) F(5) E(6) a. How many components of each kind to produce 5 product A? b. Draw operation process...
Create a Projected Balance Sheet for your business for 1 year. a. Create a pie chart showing your current assets, long-term assets, current liabilities, and long-term liabilities. b. What is your...
The following figure is a Normal probability plot of the emissions of carbon dioxide (CO 2 ) per person in 48 countries.15 Use the graph to determine if this distribution of CO 2 emissions is...
Figure P7.79 shows the $60{ }^{\circ} \mathrm{F}$ water flow rates from the branches of a main supply line. Find the total pressure drop $\left(p_{A}-p_{E} ight)$ for soldered copper pipe. Assume...
Imagen Arquitectonica of Tijuana, Mexico, is contemplating a major change in its cost structure. Currently, all of its drafting work is performed by skilled draftsmen. Alfredo Ayala, Imagens owner,...
Describe the situation from either your professional experience or your research in which unethical or fraudulent behavior occurred. If you are describing an example from experience, please do not...
The diagram shows the curve y = x 2 e2 x and its maximum point M. i. Show that the x-coordinate of M is 2. ii. Find the exact value of 2 JO xe-x dx.
The diagram shows the curve and its maximum point M. The shaded region R is enclosed by the curve, the x-axis and the lines x = 1 and x = p. i. Find the exact value of the x-coordinate of M. ii....
John Jones is an internal auditor at Dyetech, a NYSE-listed company engaged in the business of manufacturing fabric dying and printing equipment. During one internal audit Jones uncovered what he...
Classify the robots on the basis of the physical configuration.
Explain all the four phases of computer aided design.
An article in the Wall Street Journal in early 2021 reported that the economy contracted 3.5 percent last year, the largest decline since just after World War II. The article also reported that the...
Write notes on computer integrated manufacturing system and CAD/CAM.
What is NC machine? Explain its applications and limitations.
A small pump is driven by a 2 kW motor with liquid water at 150 kPa, 10C entering. Find the maximum water flow rate you can get with an exit pressure of 1 MPa and negligible kinetic energies. The...
d) For die casting processes: 1. What are the most common metals processed using die casting and discuss why other metals are not commonly die casted? 2. Which die casting machines usually have a...
Find the equation of the curve, given dy/dx and a point P on the curve. a. b. c. d. dy dx = (2x 1)3, P = 2.
Find Cambridge International AS 2 J (5-3) 5x - X d.x.
A curve is such that and the point P(1, 6) is a point on the curve. a. Find the equation of the curve. b. Find the coordinates of the stationary point on the curve and determine its nature. dy d.x...
Stack List for Payroll records a) Add a Java Project StackPayRollProject to assign the instance data of all records read from the input file PayRoll.in into a stack List to print records in the...
The following data from the just completed year are taken from the accounting records of Mason Company: Sales $ 6 5 4 , 0 0 0 Direct labor cost $ 8 9 , 0 0 0 Raw material purchases $ 1 3 3 , 0 0 0...
Find a solution to the problem that goes beyond just minimizing cost. Prepare a short write-up that describes the process you went through to find your solution and that justifies why you think it is...

When (1 + ax) 2 , where a is a positive constant, is expanded in ascending powers

Question:

Step by Step Answer:

Lets first expand 1 ax2 using the binomial theorem 1 ax2 1 2ax 232a2x2 23...View the full answer

Cambridge International AS & A Level Mathematics Pure Mathematics 2 & 3 Coursebook

Students also viewed these Mathematics questions