Solve the equation. 2x^2+7=15x

Mathematics

1 answer:

77julia77 [94]4 years ago

3 0

$2x^2+7=15x \\
2x^2-15x+7=0\\
2x^2-x-14x+7=0\\
x(2x-1)-7(2x-1)=0\\
(x-7)(2x-1)=0\\
x=7 \vee x=\frac{1}{2}
$

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First of all, we need to assume there is a typo involved, and that the expression is supposed to be ...

$\displaystyle\sum_{i=1}^{10}{5\left(\dfrac{1}{2}\right)^i}$

The values being summed look a lot like the general term of a geometric sequence:

$a_1(r^{n-1})$

The exponents in the sum range from 1 to 10, so the values being summed range from 5/2 to 5/1024. In order for that to be the case with our general term, for r = 1/2, we must have a1 = 5/2 as we let n range from 1 to 10.

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