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Find the set of values of x for which x(x-4) > 12

When solving this quadratic inequality, we should use a three-step approach. The first step is to reformat the inequality to put one side equal to zero, which is the standard format of a quadratic equation. ...
DB
Answered by Daniel B. • Maths tutor
14792 Views

Simplify (5-2√3)/(√3-1) giving your answer in the form p +q√3, where p and q are rational numbers

The trick here is to use a technique called the difference of squares. If we multiply the top and bottom of the fraction by the conjugate* of the denominator, we can remove any square root terms from the den...
AW
Answered by A W. • Maths tutor
21167 Views

Find the exact solution of the equation in its simplest form: 3^x * e^4x = e^7.

First take natural logs of both sides, giving us: ln(3 x * e 4x ) = ln(e 7 ). The RHS can be simplified using the definition of natural logs, so ln(e 7 ) = 7. We can then apply the product rule for logs (ln(...
HM
Answered by Hugo M. • Maths tutor
5980 Views

Solve 3x^2 - 4x - 6 = 0.

The at first can seem very challenging and you won't be able to tackle this question quickly using simple factorisation, which you can often do for many questions. It is best in this case then to use the Qua...
AB
Answered by Aodhan B. • Maths tutor
5249 Views

Express x^2-7x+2 in the form (x-p)^2+q where p and q are rational. Hence or otherwise find the minimum value of x^2-7x+2

For the first part, use the 'complete the square method', which gives (x-7/2) 2 -49/4+2, simplified to (x-7/2) 2 -41/4. To find the answer for the second part, set x=7/2 so that the bracketed part becomes 0,...
CW
Answered by Connaire W. • Maths tutor
5398 Views