Really Exponential

Algebra Level 2

Let $\alpha$ and $\beta$ be the two roots of the exponential equation $4 \times 8^{x+1} \times 0.25^{1+5x^2}-1=0.$ What is the value of $\alpha^2+\beta^2?$

\frac{71}{100}

\frac{73}{100}

\frac{67}{100}

\frac{69}{100}

1 solution

Saurabh Jaiswal
Jun 3, 2014

it may be written as 2^{ -10x^2+3 x+3 } = 1; so we get 10x^2-3 x-3=0; here a,b are alpha and beta !!!!! sum of roots =a+b=3/10 ; product of roots = ab=-3/10 ; a^2+b^2=(a+b)^2-2 a b ; solving we get 9/100+60/100=69/100

Really Exponential

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