Question

Fun question

Answer 1

\(\large \color{black}{\begin{align}

& \normalsize \text{Let }\ a,b,c \ \normalsize \text{be positive integers such that} \hspace{.33em}\\~\\
& \dfrac{b}{a}\ \normalsize \text{is an integer }\hspace{.33em}\\~\\
& \normalsize \text{if } \ a,b,c \ \ \normalsize \text{are in geometric progression. } \hspace{.33em}\\~\\
& \normalsize \text{and the arithmetic mean of } \ a,b,c \ \ \normalsize \text{is}\ \ (b+2) \hspace{.33em}\\~\\
& \normalsize \text{then find the value of }\ \left(\dfrac{a^2+a-14}{a+1} \right)\hspace{.33em}\\~\\
\end{align}}\)

Answer 2

It doesn't look fun

Answer 3

agreed @Afrodiddle

Answer 4

4

Answer 5

correct, how u got that

Answer 6

b/a = r(integer)

a=a
b=ar
c=ar^2

(a+ar+ar^2)/3 = ar+2
solving we get - r^2 + r(-2)+(1-6/r) = 0
solve for r
we get (- 2 +- (4-4+24/a)^(1/2))/2
1+- 1/2(24/a)^(1/2)
well r = integer therefore 24/a = perfect square

therefore a=6

we need to find (a^2 + a-14)/(a+1)
plug a = 6 and get answer = 4

Answer 7

Nice!

Answer 8

I solved it halfway in my head.

Answer 9

nice