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Solve x^2+8x-5=0 using completing the square

by completing the square we write the equation as (x+b/2)^2-b/2^2+c, in this case b=8 (the coefficient of x) and c=5 so we have (x+4)^2-16-5=0, which equals (x+4)^2-21=0. Now by rearranging we get (x+4)^2=21...
LH
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Integrate ln(x) with respect to x.

Here we can use integration by parts. Notice that ln(x) can be written as ln(x) 1, so we can integrate 1 and differentiate ln(x). Then using the formula int(u v') dx = uv - int(u' v) dx, we find that the int...
TW
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Give the general solution to the Ordinary Differential Equation: (dy/dx) + 2y/x = 3x+2

It can first be observed that this differential equation is linear, so we can solve it by multiplying the whole equation by the integrating factor. As there is no coefficient in front of the dy/dx term, we d...
VG
6469 Views

Prove by induction that for all positive integers n , f(n) = 2^(3n+1) + 3*5^(2n+1) , is divisible by 17.

Prove the base caseFor n=0, f(0)= 2 + 15 = 17Therefore, when n=0, f(n) is divisible by 17, base case is true2. Assume true for any integerAssume for n=k, f(k) is divisible by 17f(k)= 2 3k+1 + 3(5 2k+1 ) ;3. ...
SE
3679 Views

explain the eigenvalue problem

The eigenvalue problem is how we can find non-trivial solutions where x does not equal zero to the matrix equation;AX=LX (L=lambda)Values of the scalar L for which non-trivial solutions exist are called eige...
KD
4090 Views