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Solve x^2=4(x-3)^2

To solve this equation we need to expand the right hand side to get: x^2 = 4(x^2-6x+9), then we multiply whats in the bracket by 4 to get: x^2 = 4x^2 - 24x +36. We can subtract x^2 from both sides to give...

Answered by Kelsi F. • Maths tutor

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Solve 5x-2=3x+11

5x-2=3x+11

Move the (-2) to the right handside. As it crosses over the (-) becomes a (+)

5x=3x + (11+2)

Move the (+3x) to the left handside. As it crosses over the (-) becomes a (+)

Answered by Tom F. • Maths tutor

3887 Views

Consider f(x)=a/(x-1)^2-1. For which a>1 is the triangle formed by (0,0) and the intersections of f(x) with the positive x- and y-axis isosceles?

We'll first compute these intersections by setting x=0 and y=0 consecutively. This gives y=a-1 and a/(x-1)^2-1=0. Hence we find (x-1)^2=a, so x=1+-sqrt(a). As we have a>1 and we want the intersection w...

Answered by Ward V. • Maths tutor

2927 Views

How can you find the coefficients of a monic quadratic when you know only one non-real root?

We know that non-real roots appear in complex conjugate pairs. Hence when we know one root, we know both of them. Then, as we can factorise a quadratic in it's linear factors, we know our quadratic is a c...

Answered by Ward V. • Maths tutor

3772 Views

By consdering partial fractions find the integral of (1-x)/(5x-6-x^2) between x = 1 and x = 0, give your answer in an exact form.

The answer is Ln8/9, by first converting (1-x)/(5x-6-x^2) into partial fractions you get 1/(2-x) + 2/(x-3), the next step is a simple integration by inspection followed by log manipulations to get the fin...

Answered by Omar A. • Maths tutor

2816 Views