Exponential 0002

Algebra Level 2

The sum of roots to the equation 9 × 5 x 2 − 2 x + 1 = 5625 9\times 5^{x^2-2x+1} = 5625 is:

4 -2 2 -1

Aquilino Madeira by Aquilino Madeira , 60, Portugal

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1 solution

Rohit Udaiwal
Dec 11, 2015

5 x 2 − 2 x + 1 = 625 = 5 4 ⟹ x 2 − 2 x + 1 = 4 ⟹ x 2 − 2 x − 3 = 0 5^{\color{#20A900}{x^2-2x+1}}=625=5^{\color{#20A900}{4}} \\ \implies x^2-2x+1=4 \\ \implies x^2-2x-3=0 Therefore,sum of roots = − 2 1 = − 2 =\dfrac{-2}{1}=-2 .

1 Helpful 0 Interesting 0 Brilliant 0 Confused

x^2- 2x -3 = 0 ==>x=-1 v x=3

-1 + 3 = 2

Aquilino Madeira - 5 years, 6 months ago

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