Tutors Answer Your Questions about Radicals (FREE)
Question 15351: 1. Write an equation in the form y=ax^2+bx+c for the quadratic function whose graph passes through (8,0),(0,8) and (-2,0).
2. Find the roots of x^2 + (k^2+1 over k)x+1=0.
3. If (2 over x - x over 2)^2=o,evaluate x^6.
4. Find all values of k that ensure that the roots are real for x-k(x-1)(x-2)=o.
5. Find all possible values of k so that 3x^2 + kx +5 can be factored as the product of two binomial factors with integer cefficients.
6. Show that there are nine pairs of positive integers (m,n) such that m^2+3mn+2n^2-10m-20n=0.
7. The difference in the length of the hypotenuse of triangleABC and the length of the hypotenuse of triangleXYZ is 3. Hypotenuse AB=x,hypotenuse XY=square root x-1 and AB>XY. Determine the length of each hypotenuse.
Click here to see answer by khwang(438)  |
Question 15681: 9x4=25x2 -16
the x is to the 4th power, and the x is 2 the 2nd power , didn't know hot to type these right on the computer/ Its a "substitution problem so i replaced x squared with a t so i get 9t2 (t squared ) -25t +16. . i cannot figure out how to factor this.
Click here to see answer by rapaljer(4671)  |
Question 19451: I encounted in a math book recently the following equation:
x^2+x-x^2
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sqrt x^2+x+x
However, only the first two terms in the denominator are under the radical.
According to this book the above equation becomes:
x
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x(sqrt 1+1/x+1)
Again, however, the third term in the denominator is not under the radical.
Concerning the numerator, I understand why the previous equation's numerator is x. But I don't really know why and how the denominator in the previous equation is derived. The author says "Factor the x out of the denominator" but I am confused about what specific steps are needed to get the result in this denominator.
A math friend of mine suggested that I factor x^2 out of sqrt x^2+x under the radical. I assume that I could make the sqrt x^2 under the denominator first into sqrt (x^2)(1)to get x(sqrt 1... concerning this first term, but this still leaves me figuring out how the second term becomes 1/x. I imagine this is another way of saying that I do not know how x (sqrt 1+1/x...can become, in reverse, sqrt X^2+x... My math friend said that I should change the left factor of the previous denominator to sqrt x^2 and then multiply the root of x^2 times the equation in the parenthesis instead of x times the equation in the parenthesis. But if I did that, this would result in the third term,1, being x^2 rather than only 1.
So, as one can see, I am confused about this matter.
I would appreciate if someone could help clear up my confusion by explaining in a step-by-step fashion how to factor x out of the denominator in the intial equation to get the supposedly correct result in the denominator in the subsequent equation.
Click here to see answer by venugopalramana(3286) |
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