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If a quadratic equation is of the form : ax^2 +bx +c =0and has roots x1 and x2, then the following statements are true:x1+x2 = - b/ax1 x2 = c/aIn our case: x1+x2 = - 8/2 = -4and x1 x2 = 1/2Now, x1^2 + x2^2 =...

First, notice that 1/(x^2) = x^(-2)dy/dx = d/dx (x^(-2) + 4x)The derivative of the sum is the sum of the derivatives= d/dx (x^(-2)) + d/dx (4x)The derivative of x^n is nx^(n-1), for every real number n, and ...

First, we use 1 - sin(x)^2 = cos(x)^2 and get:(LHS) (cos(x)^2 + 4 sin(x)^2)/(1-sin(x)^2)= (cos(x)^2 + 4 sin(x)^2)/cos(x)^2= 1 + 4 (sin(x)/cos(x))^2= 1 + 4 tan(x)^2Now we know that the left hand side is equal...

When adding fractions, the denominators (the numbers at the bottom of the fractions) m ust be the same. If they are already the same, then you simply add the numerators (the numbers at the top of the fractio...

When a question asks you to make something the subject of an equation, it is asking you to rearrange it to get it in the form of, for example when 'p' is the subject, 'p = ....' First we want to expand the b...