a^2 - 10ab + 3b^2
*I need a lot of help with this.How do I do this one.?
Try:
(a + r b)(a + s b)
Then:
r + s = -10
r*s = 3
From the first equation:
s = -(10 + r)
Inserting in second expression:
r*(10 + r) = -3 -->
r^2 + 10 r + 3 = 0 --->
r = 5 +/- 2*sqrt[11]
You can use either solution of r, taking the other just amounts to switching r and s.
Typo:
r = -5 +/- 2*sqrt[11]
To solve the expression a^2 - 10ab + 3b^2, you can use the method of factoring.
1. Write the expression as a quadratic equation in the form of (a + r b)(a + s b), where r and s are numbers that need to be determined.
2. We have (a + r b)(a + s b) = a^2 + (r + s)ab + r s b^2.
3. Compare the quadratic equation with this expanded form to find the values of r and s.
In this case, we have a^2 - 10ab + 3b^2 as the quadratic equation, and by comparing the coefficients, we can determine that r + s = -10 and r s = 3.
4. Solve the system of equations to find the values of r and s.
From the first equation, we can solve for s as s = -(10 + r).
Substituting this value of s into the second equation gives us r(10 + r) = -3.
5. Solve the resulting quadratic equation to find the values of r.
The quadratic equation r^2 + 10r + 3 = 0 can be factored or solved using the quadratic formula. In this case, the solutions for r are r = -5 +/- 2*sqrt(11).
6. Choose either solution of r.
You can pick either r = -5 + 2*sqrt(11) or r = -5 - 2*sqrt(11). Choosing the other solution would just switch the roles of r and s.
By carefully following these steps, you can find the values r and s, and ultimately factor the expression a^2 - 10ab + 3b^2.