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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 equatio...

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 ...

First take natural logs of both sides, giving us: ln(3^x * e^4x) = ln(e⁷).  The RHS can be simplified using the definition of natural logs, so ln(e⁷) = 7.

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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 bra...

We know thst the binomial expansion formula is (1+x)ⁿ = 1+nx +(n)(n-1)(x²)/2! ...etc

Thus we want to rearrange the expression we are given into the form (1+x)ⁿ so t...