- #1
teng125
- 416
- 0
sqrt(81t^4 + 18t^2 +1).can anybody teach me how to factorise this eqn so that the sqrt can be done pls
thanx
thanx
Solving the Equation: sqrt(81t^4 + 18t^2 +1)
- Thread starter teng125
- Start date
In summary, To factorize the equation sqrt(81t^4 + 18t^2 +1), you can use the binomial theorem and substitute t^2 = r to make the equation a polynomial in t. Then, you can factorize the quadratic form and revert back to t before integrating.
- #2
teng125
- 416
- 0
i need to integrate this eqn w.r.t (t).
pls help
pls help
- #3
nazzard
Gold Member
- 100
- 0
Hello teng,
make use of the binomial theorem.
[tex](a+b)^2=a^2+2ab+b^2[/tex]
The coefficient 81 should be a good hint already.
Regards,
nazzard
make use of the binomial theorem.
[tex](a+b)^2=a^2+2ab+b^2[/tex]
The coefficient 81 should be a good hint already.
Regards,
nazzard
Last edited:
- #4
nazzard
Gold Member
- 100
- 0
teng125 said:
After you made use of the binomial theorem you will have to integrate a polynomial in t. Do you know how to do that?
Regards,
nazzard
- #5
Gagle The Terrible
- 39
- 0
If the t^4 bothers you, substitute t^2 = r in the equation and then factorize the quadratic form. Don't forget to revert to t before you integrate.
1. How do I solve the equation: sqrt(81t^4 + 18t^2 +1)?
In order to solve this equation, you will need to use the quadratic formula. First, you will need to rearrange the equation into the form ax^2 + bx + c = 0, where a = 81, b = 18, and c = 1. Then, plug these values into the quadratic formula (x = [-b ± sqrt(b^2 - 4ac)] / 2a) and solve for x. This will give you two possible solutions.
2. How do I simplify sqrt(81t^4 + 18t^2 +1)?
To simplify this expression, you can use the properties of square roots. First, you can factor out a 9 from each term inside the square root, giving you sqrt(9(9t^4 + 2t^2 + 1)). Then, you can take the square root of 9, which is 3, and move it outside of the square root. This will leave you with 3sqrt(9t^4 + 2t^2 + 1). You can also use this method to simplify any perfect square terms inside the square root.
3. Can I solve sqrt(81t^4 + 18t^2 +1) without using the quadratic formula?
Yes, you can solve this equation without using the quadratic formula. However, it may be more difficult and time-consuming. You can try to factor the expression inside the square root and see if you can find two numbers that when multiplied together give you 81t^4 and when added together give you 18t^2. This may require trial and error, but it is another method of solving the equation.
4. What is the domain and range of sqrt(81t^4 + 18t^2 +1)?
The domain of this equation is all real numbers, as there are no restrictions on the value of t that will make the expression undefined. The range includes all real numbers greater than or equal to 0, as the square root of any positive number will always be positive or 0.
5. Can I graph sqrt(81t^4 + 18t^2 +1)?
Yes, you can graph this equation. It will result in a curve, as it is a square root function. You can use a graphing calculator or software to plot points and create a visual representation of the function. This can help you see where the function intersects with the x-axis, which are the solutions to the equation.
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