# Formation and Solution of Quadratic Equations Mathematics Problem (Math Problem Sample)

reductionsa of a system of equations to quadratic equation and solving it

source..Formation and Solution of Quadratic Equations

Step 1: Formation of a quadratic equation

We are given x2+4y2=40 and xy=6. Here,

xy=6 implies that y=6x.

So, equation x2+4y2=40 can be written in terms of x as

x2+46x2=40 or x2+144x2=40 or x4-40x2+144=0.

x4-40x2+144=0 can be expressed as a quadratic equation in x2. Let z=x2 so that

z2-40z+144=0.

Step 2: Solution of a quadratic equation

To solve the above quadratic equation by factorization (Argyros, 1985), proceed as follows

z2-40z+144=z-36z-4=0.

This gives values of z as; z=4, and z=36. Since z=x2 we have the four values of x as

x=-6, x=-2, x=2, x=6.

The corresponding values of y, using y=6x are

y=-1 when x=-6, y= -3 when x=-2,

and y=3 when x=2, y=1 when x=6.

Step 3: Computation of the required result

We are required to find the value of x+2y. We have four possibilities

### Other Topics:

- Linear Equations Mathematics & Economics Math ProblemDescription: We have adopted the notation by (Anthony & Burgess, 2014), where in this case, ∆y∆x=1,500.00 $/year is the annual rate of change of salary and C is a constant denoting the starting annual salary. Using ∆y∆x=1,500.00 $/year we can write the model equation as...1 page/≈550 words| 1 Source | APA | Mathematics & Economics | Math Problem |
- Integration Mathematics & Economics Math Problem PaperDescription: The constant 3 can be taken out of integral as shown in equation (1). Applying u- substitution as shown by (Carl,2003) we let u=2x-1 and so dudx=2 which implies that dx=du2. The indefinite integral (1) now becomes 3secutanudu2=32secutanudu.(2) Applying u-substituion again, we let v=secu and so...1 page/≈550 words| 1 Source | APA | Mathematics & Economics | Math Problem |
- Probability Mathematics & Economics Math Problem PaperDescription: Probability Mathematics & Economics Math Problem Paper Solving Mathematics problems on Probability, Combinations and permutations. Probability Mathematics & Economics Math Problem Paper Solving Mathematics problems on Probability, Combinations and permutations...4 pages/≈1100 words| No Sources | APA | Mathematics & Economics | Math Problem |