Question

a,a^2 + 2 and a^3+ 10 are in G.P., then find the value(s) of a.
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Answer 1

Answer:

½ and 2

Step-by-step explanation:

(a²+2)² = a(a³+10)

on solving this we will arrive at a quadratic equation like below

2a² - 5a + 2 = 0

solve this to get answer

Answer 2

The values of a are 2 and 1/2.

Step-by-step explanation:

Consider the provided information.

If a, b and c is in G.P then $b^2=ac$

Substitute $b=a^2 + 2$ and $c=a^3+ 10$

$(a^2+2)^2=a(a^3+10)$

$a^4+4a^2+4=a^4+10a$

$a^4-a^4+4a^2+4-10a=0$

$4a^2-10a+4=0$

$2a^2-5a+2=0$

$2a^2-4a-a+2=0$

$2a(a-2)-1(a-2)=0$

$(a-2)(2a-1)=0$

$a=2\ or\ a=\frac{1}{2}$

Hence, the values of a are 2 and 1/2.

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