Hi

My name is Jennifer a student in year 11. The following problems have
me stuck and any help would be greatly appreciated seeing my text book is
doing me no favours:

3^{2a+1} - 283^{a} + 9=0

and

5^{2m} - 5^{m}=20

Thankyou for your time

Jennifer

Hi Jennifer,
Mny times solving an angebra problem is seeing a pattern. In your second problem 5^{2m} is the square of 5^{m}, so the pattern I see is

(something squared) - (something) = 20
To use more conventional mathematical notation, let x = 5^{m}, then the expression is
x^{2} - x = 20
That is
x^{2} - x - 20 = 0
which factors to give
(x - 5)(x + 4) = 0
and hence x = 5 or x = -4.
Since x = 5^{m} and 5^{m} cannot be negative, the only solution is 5^{m} = 5 and thus m = 1.

Can you now solve the first problem?

Penny